Geo Regents Review 2 - HerMathness
LINES
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1 What is the slope of a line perpendicular to the line 2 whose equation is y ! 3x " 4 ? Which statement is dem 3 construction? 1 Ms.1Menard Name: _________________ 3 # Which statement justifies this construction? 5 1 If a line is parallel t 3 1 m$1 % m$2 MG22G Regents Review #2 due date ___________ perpendicular to a t 5 1 4 # 2 m$1 % m$3 also perpendicular 2 # 3 3 3 PR & RQ 2 The set of points eq 3 all 3 work even for multiple choice questions. This will Show and counted as a quiz! endpoints of a line PS &graded RQ 4 be 4Geometry #3 perpendicular bisec 5 What is the slope of a line that is perpendicular to Regents Exam Questions by Performance Indicator: Topic Geometry Regents Exam Questions by Performance Indicator: Topic 3 Two lines are perpe www.jmap.org the line whose equation is ? 3x " 4y ! 12 www.jmap.org equidistant from a g 87 Which geometric principle is used to justify the 3 construction below? 4 Two lines are perpe 2 What isRegents the slopeExam of a line perpendicular to the line Indicator: Topic 1 Geometry Questions by Performance 96 theThe length 8 Find slope of a of lineAB perpendicular thethe linediagram below, sketch4the points that are equidistant from 1 A and B and form a vertical line 2 is 3 inches. toOn www.jmap.org y# x"4 represented the equations x"#4.5are ? 2 inches from A. Label13 whose isisypoints sketch that withThe an lines ! all points that by satisfy both conditions. whoseequation equationthe 2y!!#6x 2 3 3 2 # and 3x # 46y " 12 are 25 Find 3 an equation of the line passing through the 89 Using a compass and str 1 point # (5,4) and parallel to the line whose equation 1 SYSTEMS the4same line 2 that passes through poin 3 G.G.70: QUADRATIC-LINEAR SYSTEMS 2 parallel G.G.63: PARALLEL AND PERPENDICULAR 3 is 2x line m. [Leave all const 2 ! y " 3. 3 perpendicular # 2 LINES 4 3 # graph 29 could used to find the solution to 4 4 Which neither nor be perpendicular 3 parallel 2 equation represents a line perpendicular to the following system of equations? 93 Which 26 the Write equation of the line that" passes 3line an whose equation is 2x # 3y 12? through y " #x ! 2 Geometry Regents Exam bythe Performance Topic the point andQuestions is parallel to line whose Indicator: (6,#5) and 2y # 1 "tox one 14 The lines 3y 1# 1 "A6x # 4perpendicular ! 9 are line of two parallel 36y 1 " !4x # 12 6 What is the slope of a line to www.jmap.org 4 equation is 2x # 3y " 11. y "that x 2 is perpendicular lines is perpendicular to the other. 1 parallel 2 22y " 3x # 6 the line whose equation is ? 3x " 5y ! 4 2 Two lines are perpendicular if they intersect to 2 perpendicular 3 2y "PARALLEL !3x # 6 G.G.64: AND PERPENDICULAR 213 What equation of the adjacent line thatangles. passes through 3is anline form congruent the same 1 #point (7,3) and is parallel to the line 4 3y " !2x # 12 LINES 3 When lines are intersected by a transversal 5 parallel 4 the neither nortwo perpendicular 3 What is the PERPENDICULAR slope of a line perpendicular to the line G.G.68: BISECTOR 4x #32y " 10?and alternate interior angles are congruent, the whose equation is 2y ! #6x " 8? 2 17 What is an equation of the line that passes through 1 lines 1 are parallel. 5 271 What Write perpendicular bisector 10 theequation equationof ofthe a line that is parallel to the of #3 is an 1 y "4 x! When two lines 1 are intersected by a transversal the point (!2,5) and is perpendicular to the line 2 5 2of line 15 The equation equation y " x ! 2. The line equationwhose is y "endpoints the line segment x # 2 ? are (#1,1) and 1whose and ktheis corresponding angles are congruent, the 3 # 3 21 1 1 lines13are parallel. 3 " 5 use .y [The is optional] (7,#5) 6x #equation whose is of y "the xgrid # 5below ? ! #x 6y # " 18. Lines k and m are 2 myis"!2x of line 2 2 2 5 2 12x # y " !2 1 4 parallel 3 13 yy !" x2x" #!11 13 3y " 2x ! 11 3 2 perpendicular 2 y " !2x # 1 y " !2x 4 4 #6y ! 2x " 3 3 4the same line# 17 3 y " 2x # 9 "##! "### ! 4 neither parallel nor perpendicular 98is In diagram below, A is parked 7 miles from 7 What thethe slope of a line thatcar is perpendicular to 4 97y "Two !2xlines, ! 9 AB and CRD , are parallel and 10 car B. Sketch the points that are lineisrepresented " 2y4 miles !through 3? from car16A 11 Which inches equation represents a line parallel line that are 22 the apart. Sketch the locus oftoallthe points What an equationbyofthe theequation line thatxpasses and sketch the points that are 4 miles from car B. # ! whose equation is 2y ! 5x"#" 10? "###! 1 two #2 point and isbyparallel to the line whose lines(!2,3) represented the equations below equidistant from AB and CRD and 7 inches from16 Thethe with an ! all points that satisfy both 1 5yis!an 2xequation " 25 are2 graphed on a coordinate plane. 2 Label 18 What of the line that contains the 3 point R. Label with an ! each point that satisfies conditions. ! 4"? 12 equation is y " x #x 6y 2 Geometry Regents Exam Questions by Performance Indicator: 5y(3,!1) # 2x "and 10 is perpendicular 1Topic point to the line whose 2 both conditions. 3 # 3 www.jmap.org 4y ! 10x 2 !2 3(x ! 2) " !y ! 4 equation is y "" 12 !3x # 2? y" x 21 1 10x #" 88 14 y2y"#!3x 3 best describes the two lines? Which statement 4 G.G.31: ISOSCELES TRIANGLE THEOREM 116 In an equilateral triangle, what is the difference 2 1 The lines!2 are parallel. 5 2 y " !3x between the sum of the exterior angles and the sum 2 y" x# 2 The lines3are the3same line. 1ofare the interior angles? 12 3Twoylines represented by the equations 122 lines In the diagram of ABC below, AB % AC . The " x 3 The 3 are perpendicular. 31 180° 1 is angle 40°. other than 90°. "measure x of !B 4 3Theylines intersect at an ! y " 6x1# 10 and y " mx . For which value of m 2 4 2 y " 2 x !120° 2 1 3 3 be Geometry 90°Regents will the lines parallel? Exam Questions by Performance Indicator: " x#6 4 y Topic www.jmap.org 2 4 60° 1 !12 2 !3 On theofset coordinate below, 107 Based on the diagram below, which statement is 19 Find equation theofline passingaxes through thegraph the 3 3an105 locus of, m!A points"that arethe equidistant true?is parallel to the line whose equation is 117 In and , to , from and the lines 23 3Which lines ABC x m!B " 2x # 2 point perpendicular line whose (6,5) 4 12 s by Performance Indicator:28Topic Which equation represents theisalso perpendicular and and graph the locus of points y ! 6 y ! 2 ons by Performance Indicator: Topic . What the value of x? m!C " 3x # 4 4x # 3y " 7 and also passes through the point equation is 2y # 3x " 6. AB 3 units from the whose endpoints arey-axis. and the bisector1ofthat A(8,2)State 29 are (!5,2)? of all points that satisfy both 31 B(0,6) ?2 coordinates 1 4x # 3y " !26 ehethe following 39 Segment Line segment ABdiameter has endpoints diagram below. 43 AB is#59 the of circleA(2,"3) M. The and 32xconditions. 1 y " 4 2 4x # 3y " !14 G.G.65: AND PERPENDICULAR y for all values of x .4 What are(!4,3) the coordinates of theofmidpoint B("4,6)PARALLEL coordinates of61 A are . The coordinates M 1 LINES 3 3x # 4y " !7 y " # x ! 2 2 are are the coordinates of B? AB? . What of (1,5) 2 4 3x # 4y " 14 11 (6,7) #4 ("2,3)1 What is the measure of !A? 20 What is of a line In# equation " 3xthat # 5 ,passes m!E "through 4x $ 15 , and y "the xDEF ! 6 , m!D 2 3 118 (5,8) ! $ 1 40° 21 && and is parallel to the line whose ## m!F 14 the point (!3,!11) # &&" 2x # 10 . Which statement is true? 4 32 (!3,8) 2 50° &!12y""FE 4 ##y"1,1 " 2x 2#DF 24 Which equation represents the line parallel to the equation 4? " 1is 2x % 4 (!5,2) 3 70° line whose equation is 4x # 2y " 14 and passing 2 # 5DE " FE 13 y("1,3) " 2x 2 4 100° 3 m!E " m!F through the point (2,2)? ! $ 2 y##" 2x 1!&&5 ## 3,4 &&m!D "RSm!F 4 circle 1 y " 1!2x a ! b 44 In has endpoints 14 2diameter # O, & 25 19 3R(3a,2b y"" ! 1) x #% S(a ! 6,4b " 5). Find the a!c 2 123y "In2!2xABC 2 and2Regents Geometry Exam Questions by Performance Indicator: Topic# 6 , AB % BC . An altitude is drawn from B 4 coordinates1 of point O, in terms of a and b. 3 b!c 1 25 119 has angles in the ratio of 2:3:5. x and intersects AC at D. Which conclusion is 3 y "to AC 4Express ywww.jmap.org " your !Triangle xanswer ! PQR in simplest form. 4 d ! e true? 2 2 2 not always type ofendpoints triangle is A(3x PQR 40 If a line Which segment has #?5,3y) and the midpoint of 109 Inacute the diagram below, line p intersects line m and 1 !ABD % !CBD 1 TRIANGLES 1 , what are the coordinates of the B(x " 1,"y)line 4 y " x#1 n. 2 2 !BDA % !BDC 2 isosceles G.G.48: PYTHAGOREAN G.G.67: DISTANCE 108 In the diagram below, lines nTHEOREM and m are cut by midpoint of AB? 3 AD % BD 3 obtuse transversals p and q. 1 (x #43,2y) right AD % 111 4 Which setDC of numbers does not represent the sides 45 If2 the (2x endpoints # 2,y)of AB are A(!4,5) and B(2,!5) , of a right triangle? what the#length 3 is(2x 3,y) of AB? 1 {6,8,10} The degree measures of the angles of ABC are 124 In2isosceles triangle ABC, AB " BC . Which 14 120 2(4x34 {8,15,17} # 4,2y) statement will always be true? 2 2 represented by x, 3x, and 5x $ 54. Find the value of 3 {8,24,25} 3 1 4 m!B " m!A 3 61x. ANGLES {15,36,39} 2 m!A & m!B G.G.35: PARALLEL LINES & TRANSVERSALS 4 8 3 m!A " m!C m!C ' m!B A transversal lines. 121106In right and is 12 condition degrees DEF , intersects m!D " 90two m!FWhich 112 4 In the diagram below of ADB, m!BDA " 90, and 46 What is the between the points (!3,2) would always make two lines lessdistance than twice . the Find . parallel? m!E m!E AD " 5 2 , and AB " 2 15 . and m!2 " 7x angles 5x # 30, lines m and n are 1If m!1 Vertical are"congruent. (1,0)? cle C, QR is a diameter, value angles of x would make lines n triangles and m parallel? parallel when x equals 125 IfWhat the vertex of two isosceles are points on a coordinate 1 2 2 2 Alternate interior angles are congruent. 1 110 then the triangles must be 1 Corresponding 12.5 congruent, 3 angles are supplementary. ordinates of point R. 2 2 3 42 Same-side 80 15 12 acute interior angles are complementary. ,"4) and D(6,2) . 70 23 congruent 3 5 2 3 87.5 50 e midpoint of CD? 34 right 4 2 5 4 105 4 similar
METRY
In the of diagram of quadrilateral ABCD with 47 What is110 the length the linebelow segment with BD , m!A diagonal " 93, m!ADB " 43, endpoints (!6,4) and (2,!5) ? m!C " 3x # 5 , m!BDC " x # 19 , and 1 13 m!DBC " 2x # 6 . Determine if AB is parallel to 25 2 17 DC . Explain your reasoning. 72 3
A(7,"1) and B("3,3) . e midpoint of AB?
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145
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What is the length of BD ? 1 10
20 50 110
111 Which set of numbers does not represent the sides of a right triangle? 1 {6,8,10} 2 {8,15,17} 3 {8,24,25} 4 {15,36,39} Geometry Regents Exam Questions by Performance Indicator: Topic www.jmap.org
112 In the below below of ADB , m!BDA " 90, of the 155diagram The diagram shows the construction center of the circle circumscribed about ABC . AD " 5 2 , and AB " 2 15 .
# 30, lines m and n are
adrilateral ABCD with !ADB " 43, # 19 , and ne if AB is parallel to g.
157 Which geometric principle is used in the construction shown below?
What is the length of BD ? 1 10
1
The intersection of the angle bisectors of a
20 triangle is the center of the inscribed circle. Geometry Regents Exam Questions by Performance Indicator: Topic 3 50 2 Regents The intersection of the angleby bisectors of a Indicator: Topic Geometry Exam Questions Performance www.jmap.org www.jmap.org triangle is the center of the circumscribed 110 4 2
This construction represents how to find the
circle.
186 In the intersection diagram below of of trapezoid RSUT, RS ! TU , Geometry Regents Exam Questions by Performance Indicator: Topic 1 the angle bisectors ABC www.jmap.org X is the midpoint of RT , andofV is the midpoint of 227 189 2 the medians to the sides of ABC SU . 3 the altitudes to the sides of ABC
G.G.41: SPECIAL QUADRILATERALS 3G.G.71: The EQUATIONS intersection of OF the CIRCLES perpendicular bisectors
of the sides of a triangle is the center of the What is an equation of a diagonals circle withbisect its center at other inscribed circle. A quadrilateral whose each and a radius ofof4?the 4(!3,5) The intersection perpendicular bisectors and are perpendicular is a 136 In the diagram below of ABC , D is a point on 139 In PQR, PQ ! 8 , QR RP ! 13 . Which ! 12, and 2 2 of the sides a triangle is the center of the 4 the perpendicular bisectors of the sides of (x ! 3)angles " (yof "of5) # 16 must rhombus be true? statement1about the PQR AB, AC ! 7, AD ! 6, and BC ! 18. circumscribed circle. ABC 2 2 2 rectangle 2 (x " 3) " (y ! 5) # 16 1 m"Q $ m"P $ m"R trapezoid 2 m"Q33 $ m"R $ 2m"P (x ! 3) " (y " 5) 2 # 4 4 parallelogram 2 $ m"Q 156 In the diagram below of ABC , CD is the bisector 3 m"R4$ m"P (x " 3) " (y ! 5) 2 # 4 4 m"P $ m"R $ m"Q of !BCA, AE is the bisector of !CAB, and BG is drawn. AFEC 190 Quadrilateral ABCD, diagonal , 228 Given: Which equation represents the circle whose center 140 In ABCAE and .AC Which 7,and BC !& 8, AC is, AB whose radius (!2,3) $!FC DE!is&95? , BF , AC , %1 $ %2 list has the angles of 2 ABC in 2 order from smallest Prove: parallelogram. 2) " (yis"a3) #5 1 (x !ABCD to largest? If RS ! 30 and XV ! 44, what is the length of TU ? 2 2 2 (x " 2) " (y ! 3) # 5 1 "A,"B,"C 1 37 2 "B,"A,"C 3 (x " 2) 2 " (y ! 3) 2 # 25 2 58 3 "C,"B,"A 4 (x ! 2) 2 " (y " 3) 2 # 25 74 of DB could be The3length 4 "C,"A,"B 1 45 118 2 12 229 What is an equation of a circle with center (7,!3) 3 19 141 In the diagramradius below4?of ABC with side AC statement must be true? 1874 In25the Which diagram below of isosceles trapezoid DEFG, extended and through D, 2m"A ! 372 and 1 DG " EG 23 1 (x ! 7) " (y " 3) # 4 DE"!BG 4x " 2 , EF ! 3x # 2, FG ! 5x " 3, side of2 ABC is the m"BCD ! 117 . Which ions by Performance Indicator: Topic DE ! 2GF ,AG 2 (x " 7) 2 your " (y !answer. 3) # 4 longest side? Justify . Find the value of x. and GD ! 2x # 5 3 !AEB # !AEC G.G.34: ANGLE SIDE RELATIONSHIP 2 7) 2 " (yis" a3)parallelogram. # 16 3 (x ! JKLM 4 !DBG # !EBG 191 Given: 153 On the set of axes below, graph and label DEF 2 2 ABC , DE is a 137 In ABC , m"A ! 95, m"B ! 50, and m"C ! 35. 4 (x " 7) " (y ! 3) # 16 JM $ LN with vertices at D("4,"4) , E("2,2) , and F(8,"2) . If E ! 7 , AB ! 10, and Which expression correctly relates the lengths of %LMN $ %LNM er of ABC . EF and H is the midpoint of G the is the midpoint sides of thisof triangle? Prove: JKLM is a rhombus. DF1Geometry , state coordinates of G and H and label 230 Topic What is an equation of the circle with a radius of 5 ABthe # BC # CA Exam Regents Questions by Performance Indicator: and center at (1,!4)? 2www.jmap.org AB # # BC each point onAC your graph. Explain why GH ! DE . 3 AC # BC # AB 32 1 (x " 1) 2 " (y ! 4) 2 # 5 4 BCG.G.27: # AC # AB TRIANGLE PROOFS 337 2In the (x !diagram 1) 2 " (y below, " 4) 2 # PA 5 and PB are tangent to
334 Given: ABC and EDC , C is the midpoint of 138 In scalene triangle ABC, m"B ! 45 and m"C ! 55. and AE What isBD the order of the sides in length, from to shortest? 188longest The Prove: diagram ABbelow ! DE shows isosceles trapezoid AB, BCwith 1 ABCD , ACAB ! DC and AD $ BC . If BC , AC ,!AB 2 m%BAD 2x and m%BCD ! 3x # 5 , find m%BAD . 3 AC , BC , AB 4 BC , AB, AC
elow, AB ! 10, BC ! 14 , imeter of the triangle midpoints of the sides of
232 Write an equation of has endpoints A(!4,2 the grid below is opt
G.G.72: EQUATION
233 Which equation repr graph below?
2 2 OB and (x "O,1)OA " (y ! 4) #are 25 radii, and OP intersects 3circle 2at C. Prove: the circle "AOP ! "BOP 4 (x ! 1) " (y " 4) 2 # 25
231 The diameter of a circle has endpoints at (!2,3) and (6,3). What is an equation of the circle? 1 2 3 4
(x ! 2) 2 " (y ! 3) 2 (x ! 2) 2 " (y ! 3) 2 (x " 2) 2 " (y " 3) 2 (x " 2) 2 " (y " 3) 2
# 16 #4 # 16 #4
1 2 3 4
G.G.27: QUADRILATERAL PROOFS
335 Given: Quadrilateral ABCD with AB ! CD, estions by Performance Indicator: Topic G.G.21: CENTROID, ORTHOCENTER, AD ! BC , and diagonal BD is drawn INCENTER AND "BDC CIRCUMCENTER Prove: ! "ABD 28 175 Which statement is true about every parallelogram? GRAMS
38 154 In1which doare thecongruent. three altitudes intersect All triangle four sides outside theinterior triangle? 2 The angles are all congruent. G.G.27: CIRCLE PROOFS 1 3 a Two rightpairs triangle of opposite sides are congruent. estions by Performance Indicator: 2Topic 4 anThe diagonals acute triangleare perpendicular to each other. In the diagram below, quadrilateral ABCD is 3 336 an obtuse triangle inscribedtriangle in circle O, AB ! DC , and diagonals AC 4 an equilateral Questions by Performance176 Indicator: Topic In the diagram below, parallelogram ABCD has and BD are drawn. Prove that ACD ! BDC . diagonals AC and BD that intersect at point E. 170 What is the measure of each interior angle of a regular hexagon? ND EXTERIOR ANGLES 1 60! 2 120! ? !2 3 135! gram below is formed by 4 270!
G.G.44: SIMILARITY PROOFS 338 In the diagram below of PRT , Q is a point on 48 PR , S is a point on TR, QS is drawn, and "RPT ! "RSQ.
parallelogram ABCD with m!1 " 45 and
parallelogram STUV, and TU " 4x $ 3.
31
expression is not 171 Which In the diagram below ofalways regulartrue? pentagon ABCDE, 1EB !DAE % !BCE is drawn. 2 !DEC % !BEA 3 AC % DB 4 DE % EB G.G.39: PARALLELOGRAMS 177 In the diagram below of rhombus ABCD,
Which reason justifies the conclusion that PRT # SRQ? 1 AA 2 ASA 3 SAS 4 SSS
Geo Regents Review 2.docx
(x " 5) 2 " (y ! 1) (x " 5) 2 " (y ! 1) (x ! 5) 2 " (y " 1) (x ! 5) 2 " (y " 1)
Ms. Menard MG22G
Name: _________________ Regents Review #2 due date ___________
Show all work even for multiple choice questions. This will be graded and counted as a quiz!
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1 What is the slope of a line perpendicular to the line 2 whose equation is y ! 3x " 4 ? Which statement is dem 3 construction? 1 Ms.1Menard Name: _________________ 3 # Which statement justifies this construction? 5 1 If a line is parallel t 3 1 m$1 % m$2 MG22G Regents Review #2 due date ___________ perpendicular to a t 5 1 4 # 2 m$1 % m$3 also perpendicular 2 # 3 3 3 PR & RQ 2 The set of points eq 3 all 3 work even for multiple choice questions. This will Show and counted as a quiz! endpoints of a line PS &graded RQ 4 be 4Geometry #3 perpendicular bisec 5 What is the slope of a line that is perpendicular to Regents Exam Questions by Performance Indicator: Topic Geometry Regents Exam Questions by Performance Indicator: Topic 3 Two lines are perpe www.jmap.org the line whose equation is ? 3x " 4y ! 12 www.jmap.org equidistant from a g 87 Which geometric principle is used to justify the 3 construction below? 4 Two lines are perpe 2 What isRegents the slopeExam of a line perpendicular to the line Indicator: Topic 1 Geometry Questions by Performance 96 theThe length 8 Find slope of a of lineAB perpendicular thethe linediagram below, sketch4the points that are equidistant from 1 A and B and form a vertical line 2 is 3 inches. toOn www.jmap.org y# x"4 represented the equations x"#4.5are ? 2 inches from A. Label13 whose isisypoints sketch that withThe an lines ! all points that by satisfy both conditions. whoseequation equationthe 2y!!#6x 2 3 3 2 # and 3x # 46y " 12 are 25 Find 3 an equation of the line passing through the 89 Using a compass and str 1 point # (5,4) and parallel to the line whose equation 1 SYSTEMS the4same line 2 that passes through poin 3 G.G.70: QUADRATIC-LINEAR SYSTEMS 2 parallel G.G.63: PARALLEL AND PERPENDICULAR 3 is 2x line m. [Leave all const 2 ! y " 3. 3 perpendicular # 2 LINES 4 3 # graph 29 could used to find the solution to 4 4 Which neither nor be perpendicular 3 parallel 2 equation represents a line perpendicular to the following system of equations? 93 Which 26 the Write equation of the line that" passes 3line an whose equation is 2x # 3y 12? through y " #x ! 2 Geometry Regents Exam bythe Performance Topic the point andQuestions is parallel to line whose Indicator: (6,#5) and 2y # 1 "tox one 14 The lines 3y 1# 1 "A6x # 4perpendicular ! 9 are line of two parallel 36y 1 " !4x # 12 6 What is the slope of a line to www.jmap.org 4 equation is 2x # 3y " 11. y "that x 2 is perpendicular lines is perpendicular to the other. 1 parallel 2 22y " 3x # 6 the line whose equation is ? 3x " 5y ! 4 2 Two lines are perpendicular if they intersect to 2 perpendicular 3 2y "PARALLEL !3x # 6 G.G.64: AND PERPENDICULAR 213 What equation of the adjacent line thatangles. passes through 3is anline form congruent the same 1 #point (7,3) and is parallel to the line 4 3y " !2x # 12 LINES 3 When lines are intersected by a transversal 5 parallel 4 the neither nortwo perpendicular 3 What is the PERPENDICULAR slope of a line perpendicular to the line G.G.68: BISECTOR 4x #32y " 10?and alternate interior angles are congruent, the whose equation is 2y ! #6x " 8? 2 17 What is an equation of the line that passes through 1 lines 1 are parallel. 5 271 What Write perpendicular bisector 10 theequation equationof ofthe a line that is parallel to the of #3 is an 1 y "4 x! When two lines 1 are intersected by a transversal the point (!2,5) and is perpendicular to the line 2 5 2of line 15 The equation equation y " x ! 2. The line equationwhose is y "endpoints the line segment x # 2 ? are (#1,1) and 1whose and ktheis corresponding angles are congruent, the 3 # 3 21 1 1 lines13are parallel. 3 " 5 use .y [The is optional] (7,#5) 6x #equation whose is of y "the xgrid # 5below ? ! #x 6y # " 18. Lines k and m are 2 myis"!2x of line 2 2 2 5 2 12x # y " !2 1 4 parallel 3 13 yy !" x2x" #!11 13 3y " 2x ! 11 3 2 perpendicular 2 y " !2x # 1 y " !2x 4 4 #6y ! 2x " 3 3 4the same line# 17 3 y " 2x # 9 "##! "### ! 4 neither parallel nor perpendicular 98is In diagram below, A is parked 7 miles from 7 What thethe slope of a line thatcar is perpendicular to 4 97y "Two !2xlines, ! 9 AB and CRD , are parallel and 10 car B. Sketch the points that are lineisrepresented " 2y4 miles !through 3? from car16A 11 Which inches equation represents a line parallel line that are 22 the apart. Sketch the locus oftoallthe points What an equationbyofthe theequation line thatxpasses and sketch the points that are 4 miles from car B. # ! whose equation is 2y ! 5x"#" 10? "###! 1 two #2 point and isbyparallel to the line whose lines(!2,3) represented the equations below equidistant from AB and CRD and 7 inches from16 Thethe with an ! all points that satisfy both 1 5yis!an 2xequation " 25 are2 graphed on a coordinate plane. 2 Label 18 What of the line that contains the 3 point R. Label with an ! each point that satisfies conditions. ! 4"? 12 equation is y " x #x 6y 2 Geometry Regents Exam Questions by Performance Indicator: 5y(3,!1) # 2x "and 10 is perpendicular 1Topic point to the line whose 2 both conditions. 3 # 3 www.jmap.org 4y ! 10x 2 !2 3(x ! 2) " !y ! 4 equation is y "" 12 !3x # 2? y" x 21 1 10x #" 88 14 y2y"#!3x 3 best describes the two lines? Which statement 4 G.G.31: ISOSCELES TRIANGLE THEOREM 116 In an equilateral triangle, what is the difference 2 1 The lines!2 are parallel. 5 2 y " !3x between the sum of the exterior angles and the sum 2 y" x# 2 The lines3are the3same line. 1ofare the interior angles? 12 3Twoylines represented by the equations 122 lines In the diagram of ABC below, AB % AC . The " x 3 The 3 are perpendicular. 31 180° 1 is angle 40°. other than 90°. "measure x of !B 4 3Theylines intersect at an ! y " 6x1# 10 and y " mx . For which value of m 2 4 2 y " 2 x !120° 2 1 3 3 be Geometry 90°Regents will the lines parallel? Exam Questions by Performance Indicator: " x#6 4 y Topic www.jmap.org 2 4 60° 1 !12 2 !3 On theofset coordinate below, 107 Based on the diagram below, which statement is 19 Find equation theofline passingaxes through thegraph the 3 3an105 locus of, m!A points"that arethe equidistant true?is parallel to the line whose equation is 117 In and , to , from and the lines 23 3Which lines ABC x m!B " 2x # 2 point perpendicular line whose (6,5) 4 12 s by Performance Indicator:28Topic Which equation represents theisalso perpendicular and and graph the locus of points y ! 6 y ! 2 ons by Performance Indicator: Topic . What the value of x? m!C " 3x # 4 4x # 3y " 7 and also passes through the point equation is 2y # 3x " 6. AB 3 units from the whose endpoints arey-axis. and the bisector1ofthat A(8,2)State 29 are (!5,2)? of all points that satisfy both 31 B(0,6) ?2 coordinates 1 4x # 3y " !26 ehethe following 39 Segment Line segment ABdiameter has endpoints diagram below. 43 AB is#59 the of circleA(2,"3) M. The and 32xconditions. 1 y " 4 2 4x # 3y " !14 G.G.65: AND PERPENDICULAR y for all values of x .4 What are(!4,3) the coordinates of theofmidpoint B("4,6)PARALLEL coordinates of61 A are . The coordinates M 1 LINES 3 3x # 4y " !7 y " # x ! 2 2 are are the coordinates of B? AB? . What of (1,5) 2 4 3x # 4y " 14 11 (6,7) #4 ("2,3)1 What is the measure of !A? 20 What is of a line In# equation " 3xthat # 5 ,passes m!E "through 4x $ 15 , and y "the xDEF ! 6 , m!D 2 3 118 (5,8) ! $ 1 40° 21 && and is parallel to the line whose ## m!F 14 the point (!3,!11) # &&" 2x # 10 . Which statement is true? 4 32 (!3,8) 2 50° &!12y""FE 4 ##y"1,1 " 2x 2#DF 24 Which equation represents the line parallel to the equation 4? " 1is 2x % 4 (!5,2) 3 70° line whose equation is 4x # 2y " 14 and passing 2 # 5DE " FE 13 y("1,3) " 2x 2 4 100° 3 m!E " m!F through the point (2,2)? ! $ 2 y##" 2x 1!&&5 ## 3,4 &&m!D "RSm!F 4 circle 1 y " 1!2x a ! b 44 In has endpoints 14 2diameter # O, & 25 19 3R(3a,2b y"" ! 1) x #% S(a ! 6,4b " 5). Find the a!c 2 123y "In2!2xABC 2 and2Regents Geometry Exam Questions by Performance Indicator: Topic# 6 , AB % BC . An altitude is drawn from B 4 coordinates1 of point O, in terms of a and b. 3 b!c 1 25 119 has angles in the ratio of 2:3:5. x and intersects AC at D. Which conclusion is 3 y "to AC 4Express ywww.jmap.org " your !Triangle xanswer ! PQR in simplest form. 4 d ! e true? 2 2 2 not always type ofendpoints triangle is A(3x PQR 40 If a line Which segment has #?5,3y) and the midpoint of 109 Inacute the diagram below, line p intersects line m and 1 !ABD % !CBD 1 TRIANGLES 1 , what are the coordinates of the B(x " 1,"y)line 4 y " x#1 n. 2 2 !BDA % !BDC 2 isosceles G.G.48: PYTHAGOREAN G.G.67: DISTANCE 108 In the diagram below, lines nTHEOREM and m are cut by midpoint of AB? 3 AD % BD 3 obtuse transversals p and q. 1 (x #43,2y) right AD % 111 4 Which setDC of numbers does not represent the sides 45 If2 the (2x endpoints # 2,y)of AB are A(!4,5) and B(2,!5) , of a right triangle? what the#length 3 is(2x 3,y) of AB? 1 {6,8,10} The degree measures of the angles of ABC are 124 In2isosceles triangle ABC, AB " BC . Which 14 120 2(4x34 {8,15,17} # 4,2y) statement will always be true? 2 2 represented by x, 3x, and 5x $ 54. Find the value of 3 {8,24,25} 3 1 4 m!B " m!A 3 61x. ANGLES {15,36,39} 2 m!A & m!B G.G.35: PARALLEL LINES & TRANSVERSALS 4 8 3 m!A " m!C m!C ' m!B A transversal lines. 121106In right and is 12 condition degrees DEF , intersects m!D " 90two m!FWhich 112 4 In the diagram below of ADB, m!BDA " 90, and 46 What is the between the points (!3,2) would always make two lines lessdistance than twice . the Find . parallel? m!E m!E AD " 5 2 , and AB " 2 15 . and m!2 " 7x angles 5x # 30, lines m and n are 1If m!1 Vertical are"congruent. (1,0)? cle C, QR is a diameter, value angles of x would make lines n triangles and m parallel? parallel when x equals 125 IfWhat the vertex of two isosceles are points on a coordinate 1 2 2 2 Alternate interior angles are congruent. 1 110 then the triangles must be 1 Corresponding 12.5 congruent, 3 angles are supplementary. ordinates of point R. 2 2 3 42 Same-side 80 15 12 acute interior angles are complementary. ,"4) and D(6,2) . 70 23 congruent 3 5 2 3 87.5 50 e midpoint of CD? 34 right 4 2 5 4 105 4 similar
METRY
In the of diagram of quadrilateral ABCD with 47 What is110 the length the linebelow segment with BD , m!A diagonal " 93, m!ADB " 43, endpoints (!6,4) and (2,!5) ? m!C " 3x # 5 , m!BDC " x # 19 , and 1 13 m!DBC " 2x # 6 . Determine if AB is parallel to 25 2 17 DC . Explain your reasoning. 72 3
A(7,"1) and B("3,3) . e midpoint of AB?
4
145
2 3 4
22
7
What is the length of BD ? 1 10
20 50 110
111 Which set of numbers does not represent the sides of a right triangle? 1 {6,8,10} 2 {8,15,17} 3 {8,24,25} 4 {15,36,39} Geometry Regents Exam Questions by Performance Indicator: Topic www.jmap.org
112 In the below below of ADB , m!BDA " 90, of the 155diagram The diagram shows the construction center of the circle circumscribed about ABC . AD " 5 2 , and AB " 2 15 .
# 30, lines m and n are
adrilateral ABCD with !ADB " 43, # 19 , and ne if AB is parallel to g.
157 Which geometric principle is used in the construction shown below?
What is the length of BD ? 1 10
1
The intersection of the angle bisectors of a
20 triangle is the center of the inscribed circle. Geometry Regents Exam Questions by Performance Indicator: Topic 3 50 2 Regents The intersection of the angleby bisectors of a Indicator: Topic Geometry Exam Questions Performance www.jmap.org www.jmap.org triangle is the center of the circumscribed 110 4 2
This construction represents how to find the
circle.
186 In the intersection diagram below of of trapezoid RSUT, RS ! TU , Geometry Regents Exam Questions by Performance Indicator: Topic 1 the angle bisectors ABC www.jmap.org X is the midpoint of RT , andofV is the midpoint of 227 189 2 the medians to the sides of ABC SU . 3 the altitudes to the sides of ABC
G.G.41: SPECIAL QUADRILATERALS 3G.G.71: The EQUATIONS intersection of OF the CIRCLES perpendicular bisectors
of the sides of a triangle is the center of the What is an equation of a diagonals circle withbisect its center at other inscribed circle. A quadrilateral whose each and a radius ofof4?the 4(!3,5) The intersection perpendicular bisectors and are perpendicular is a 136 In the diagram below of ABC , D is a point on 139 In PQR, PQ ! 8 , QR RP ! 13 . Which ! 12, and 2 2 of the sides a triangle is the center of the 4 the perpendicular bisectors of the sides of (x ! 3)angles " (yof "of5) # 16 must rhombus be true? statement1about the PQR AB, AC ! 7, AD ! 6, and BC ! 18. circumscribed circle. ABC 2 2 2 rectangle 2 (x " 3) " (y ! 5) # 16 1 m"Q $ m"P $ m"R trapezoid 2 m"Q33 $ m"R $ 2m"P (x ! 3) " (y " 5) 2 # 4 4 parallelogram 2 $ m"Q 156 In the diagram below of ABC , CD is the bisector 3 m"R4$ m"P (x " 3) " (y ! 5) 2 # 4 4 m"P $ m"R $ m"Q of !BCA, AE is the bisector of !CAB, and BG is drawn. AFEC 190 Quadrilateral ABCD, diagonal , 228 Given: Which equation represents the circle whose center 140 In ABCAE and .AC Which 7,and BC !& 8, AC is, AB whose radius (!2,3) $!FC DE!is&95? , BF , AC , %1 $ %2 list has the angles of 2 ABC in 2 order from smallest Prove: parallelogram. 2) " (yis"a3) #5 1 (x !ABCD to largest? If RS ! 30 and XV ! 44, what is the length of TU ? 2 2 2 (x " 2) " (y ! 3) # 5 1 "A,"B,"C 1 37 2 "B,"A,"C 3 (x " 2) 2 " (y ! 3) 2 # 25 2 58 3 "C,"B,"A 4 (x ! 2) 2 " (y " 3) 2 # 25 74 of DB could be The3length 4 "C,"A,"B 1 45 118 2 12 229 What is an equation of a circle with center (7,!3) 3 19 141 In the diagramradius below4?of ABC with side AC statement must be true? 1874 In25the Which diagram below of isosceles trapezoid DEFG, extended and through D, 2m"A ! 372 and 1 DG " EG 23 1 (x ! 7) " (y " 3) # 4 DE"!BG 4x " 2 , EF ! 3x # 2, FG ! 5x " 3, side of2 ABC is the m"BCD ! 117 . Which ions by Performance Indicator: Topic DE ! 2GF ,AG 2 (x " 7) 2 your " (y !answer. 3) # 4 longest side? Justify . Find the value of x. and GD ! 2x # 5 3 !AEB # !AEC G.G.34: ANGLE SIDE RELATIONSHIP 2 7) 2 " (yis" a3)parallelogram. # 16 3 (x ! JKLM 4 !DBG # !EBG 191 Given: 153 On the set of axes below, graph and label DEF 2 2 ABC , DE is a 137 In ABC , m"A ! 95, m"B ! 50, and m"C ! 35. 4 (x " 7) " (y ! 3) # 16 JM $ LN with vertices at D("4,"4) , E("2,2) , and F(8,"2) . If E ! 7 , AB ! 10, and Which expression correctly relates the lengths of %LMN $ %LNM er of ABC . EF and H is the midpoint of G the is the midpoint sides of thisof triangle? Prove: JKLM is a rhombus. DF1Geometry , state coordinates of G and H and label 230 Topic What is an equation of the circle with a radius of 5 ABthe # BC # CA Exam Regents Questions by Performance Indicator: and center at (1,!4)? 2www.jmap.org AB # # BC each point onAC your graph. Explain why GH ! DE . 3 AC # BC # AB 32 1 (x " 1) 2 " (y ! 4) 2 # 5 4 BCG.G.27: # AC # AB TRIANGLE PROOFS 337 2In the (x !diagram 1) 2 " (y below, " 4) 2 # PA 5 and PB are tangent to
334 Given: ABC and EDC , C is the midpoint of 138 In scalene triangle ABC, m"B ! 45 and m"C ! 55. and AE What isBD the order of the sides in length, from to shortest? 188longest The Prove: diagram ABbelow ! DE shows isosceles trapezoid AB, BCwith 1 ABCD , ACAB ! DC and AD $ BC . If BC , AC ,!AB 2 m%BAD 2x and m%BCD ! 3x # 5 , find m%BAD . 3 AC , BC , AB 4 BC , AB, AC
elow, AB ! 10, BC ! 14 , imeter of the triangle midpoints of the sides of
232 Write an equation of has endpoints A(!4,2 the grid below is opt
G.G.72: EQUATION
233 Which equation repr graph below?
2 2 OB and (x "O,1)OA " (y ! 4) #are 25 radii, and OP intersects 3circle 2at C. Prove: the circle "AOP ! "BOP 4 (x ! 1) " (y " 4) 2 # 25
231 The diameter of a circle has endpoints at (!2,3) and (6,3). What is an equation of the circle? 1 2 3 4
(x ! 2) 2 " (y ! 3) 2 (x ! 2) 2 " (y ! 3) 2 (x " 2) 2 " (y " 3) 2 (x " 2) 2 " (y " 3) 2
# 16 #4 # 16 #4
1 2 3 4
G.G.27: QUADRILATERAL PROOFS
335 Given: Quadrilateral ABCD with AB ! CD, estions by Performance Indicator: Topic G.G.21: CENTROID, ORTHOCENTER, AD ! BC , and diagonal BD is drawn INCENTER AND "BDC CIRCUMCENTER Prove: ! "ABD 28 175 Which statement is true about every parallelogram? GRAMS
38 154 In1which doare thecongruent. three altitudes intersect All triangle four sides outside theinterior triangle? 2 The angles are all congruent. G.G.27: CIRCLE PROOFS 1 3 a Two rightpairs triangle of opposite sides are congruent. estions by Performance Indicator: 2Topic 4 anThe diagonals acute triangleare perpendicular to each other. In the diagram below, quadrilateral ABCD is 3 336 an obtuse triangle inscribedtriangle in circle O, AB ! DC , and diagonals AC 4 an equilateral Questions by Performance176 Indicator: Topic In the diagram below, parallelogram ABCD has and BD are drawn. Prove that ACD ! BDC . diagonals AC and BD that intersect at point E. 170 What is the measure of each interior angle of a regular hexagon? ND EXTERIOR ANGLES 1 60! 2 120! ? !2 3 135! gram below is formed by 4 270!
G.G.44: SIMILARITY PROOFS 338 In the diagram below of PRT , Q is a point on 48 PR , S is a point on TR, QS is drawn, and "RPT ! "RSQ.
parallelogram ABCD with m!1 " 45 and
parallelogram STUV, and TU " 4x $ 3.
31
expression is not 171 Which In the diagram below ofalways regulartrue? pentagon ABCDE, 1EB !DAE % !BCE is drawn. 2 !DEC % !BEA 3 AC % DB 4 DE % EB G.G.39: PARALLELOGRAMS 177 In the diagram below of rhombus ABCD,
Which reason justifies the conclusion that PRT # SRQ? 1 AA 2 ASA 3 SAS 4 SSS
Geo Regents Review 2.docx
(x " 5) 2 " (y ! 1) (x " 5) 2 " (y ! 1) (x ! 5) 2 " (y " 1) (x ! 5) 2 " (y " 1)
Ms. Menard MG22G
Name: _________________ Regents Review #2 due date ___________
Show all work even for multiple choice questions. This will be graded and counted as a quiz!
