Geo Regents Review 6 - HerMathness
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4 Ms. Menard Name: _________________ 3 Geometry Regents Exam Questions by Performance Indicator: Topic 3 MG22G 4www.jmap.org Regents Review #6 due date ___________ 4 # 3 48 In circle O, a diameter has endpoints (!5,4) and G.G.1: PLANES Show all work even for multiple choice questions. This will be graded and counted as a quiz! (3,!6). What is the length of the diameter? 53 Lines k 1 and k 2 intersect at point E. Line m is 1 of a2 line that is perpendicular to 6 What is the slope perpendicular to lines k 1 and k 2 at point E. the line whose2 equation 2 2 is 3x " 5y ! 4? 3 10 3 1 # mance the lineIndicator: Topic 5 4 2 41 3 2 5 line 1 5 What is the of the line y #segment x " 4 whose 13 3The #lines49represented bylength the equations 2 ? 3 endpoints are A(!1,9) and B(7,4) and 3x 5 # 6y " 12 are 4 61 1 1 3the same line 2 89 2 parallel LAR 205 3 3 perpendicular 7 What is the slope of anor line that is perpendicular to 4 neither parallel 4 233theperpendicular mance Indicator: Topic the line represented by equation x " 2y ! 3? ular to 1 #2 2The 2is and 2yofsystem are 14 What lines 3y # 1 "of6x # following 4length # the 1 " line xof! 9segment What isthe the whose 34 the50 solution x 1 1 parallel equations? endpoints are and ? (1,!4) (9,2) 3 # 2 Which statement is always true? 2 perpendicular 1 y !5 (x # 3) 2 " 4 1 1 Lines k 1 and k 2 are perpendicular. 3 the same line 4 2 y !2 2x 17 #5 2 neither parallel 2 Line m is parallel to the plane determined by 3 10 nor perpendicular 14 (0,"4) lines k 1 and k 2 . 2 ("4,0) 4 2 26 3 Line m is perpendicular to the plane 3 ("4,"3) and (0,5) l to the 1 determined by lines k 1 and k 2 . 4The("3,"4) and of (5,0) 15 equation line k is . The equation y " x ! 2 Geometry Exam by by Indicator: Performance 1 Geometry 3Questions RegentsRegents Exam Questions Performance Topic Indicator: Topic 51 What is the length, to the nearest tenth, of the line 4 Line m is coplanar with lines k 1 and k 2 . www.jmap.org www.jmap.org of line m is !2x # 6y " 18. Lines k and m are segment joining the points (!4,2) and (146,52)? 35 Solve the following system of equations 1 parallel 1 a compass 141.4 82 graphically. The diagram below shows theand construction of the construct 84 the One step in a construction uses CONSTRUCTIONS the endpoints of AB Using straightedge, G.G.18: 2 79perpendicular f 2bisector !, lines and n intersect at point A. If 54 the In same planeradii. 2150.5 toall create arcs with Them arcs AB. perpendicular of 2x " 4x ! y # 1 angle bisector of shown below. [Leave !ABC 3 the same3line151.9 intersect above and below the segment. Whattoisline m and line n at point line k is perpendicular 81 Which diagram shows the construction of the construction 4 neither parallel x #nor ymarks.] ! perpendicular 1 4 158.1 the relationship of AB linek connecting the A, and thentheline is of AB? points of intersection1perpendicular of these arcs? inbisector contained plane ! the line 1 collinear 2 parallel to plane ! 16 The two lines represented by the equations below 2 . congruent 52 The endpoints of PQ are P(!3,1) and Q(4,25) are graphed on a coordinate plane. 3 parallel 3 perpendicular to plane ! Find thex length # 6y "of 12PQ . 4 perpendicular 4 skew to plane ! 3(x ! 2) " !y ! 4 85 On the diagram of ABC shown below, use a Which statement best describes the two lines? compass and straightedge to construct the 1 The lines are parallel. iven perpendicular bisector of AC . [Leave all 2 The lines are the same line. construction marks.] 3 The lines are perpendicular. 1 4 The lines intersect at an angle other than 90°. e of m Which statement is not true? 1 AC ! CB 1 2 CB ! AB 80 On2the diagram below, use a compass and 3 AC ! 2AB straightedge to construct the bisector of !ABC . 4 AC " CB ! AB
tion to
[Leave all construction marks.]
83 Line segment AB is shown in the diagram below.
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Which two sets of construction marks, labeled I, II, III, and IV, are part of the construction of the perpendicular bisector of line segment AB? 1 I and II 2 I and III 3 II and III 4 II and IV
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120° 90° 60°
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The intersection of the angle bisectors of a 248 A prism has volume of AC and BD 182 G triangle is the of the circumscribed 178center Inrectangular rhombus ABCD, thea diagonals 2 3x ! 18x !at24E.. Its a length x ,!what 2 andisa the re circle. intersect If base AE !has 5 and BE !of12 width of 3. Which expression represents the height m 3 The intersection of the perpendicular bisectors length of AB? of the prism? 1 of the sides of a triangle is the center of the 1 7 1 x!4 2 inscribed circle. 2 10 2 x!2 3 4 The intersection of the perpendicular bisectors Geometry Exam Questions by Performance Indicator: Topic 33 Regents 313 4 of the sides of a triangle 2 is the center of the 4 17 www.jmap.org 4 x ! 6x ! 8 circumscribed circle. What is the measure of !A? 197 In th 1 40° 179 CONICS G In the diagram below, quadrilateral STAR is a and 2 50° G.G.49: CHORDS rhombus with diagonals SA and TR intersecting at 183chor If 3 70° E. ST ! 3x " 30, SR ! 8x # 5, SE ! 3z, TE ! 5z " 5, ea the diagram below, ABC is inscribed in circle 4 100°196 InAE ! 4z # 8, m$RTA ! 5y # 2, and 1 P. The distances from the center of circle P to each Find SR, RT, and m$TAS . 52 m$TAS 9y " 8 . are 2 side of the!triangle shown. 3 123 In ABC , AB % BC . An altitude is drawn from B 4
117 In ABC , m!A " x , m!B " 2x # 2 , and What is the value of the x? m!C " 3x # 4 . represents This construction how to find 1 29 of intersection 31angle bisectors of ABC 12 the 59medians to the sides of ABC 23 the 34 the 61altitudes to the sides of ABC 4
1 20 of 6 cm 2 60 3 120 the heig Geometry Regents Exam Questions by Performance Indicator: Top The intersection of angle bisectors of a 4 the 240 triangle is www.jmap.org the center of the inscribed circle.
the perpendicular bisectors of the sides of ABC
118 In DEF , m!D " 3x # 5 , m!E " 4x $ 15 , and m!F " 2x # 10 . Which statement is true? 156 In1 the DF diagram " FEbelow of ABC , CD is the bisector AEFE , is the bisector of !CAB, and BG is of2 !BCA DE " drawn. 3 m!E " m!F 4 m!D " m!F
to AC and intersects AC at D. Which conclusion is not always true? 1 !ABD % !CBD 2 !BDA % !BDC 3 AD % BD 4 AD % DC
119 Triangle PQR has angles in the ratio of 2:3:5. Which type of triangle is PQR? 1 acute 2 isosceles 3 obtuse 4 right
184 Is BD va 1 Wha Which statement must be true? 2 1 1 DG " EG Geometry Regents Exam Questions by Performance Indicator: Topi 23 " BGmeasures of the angles of ABC are 120 2TheAG degree 124 In isosceles triangle ABC, AB " BC . Which www.jmap.org 3 3represented !AEB # !AEC Geometry Regents Exam Performance Topic by x, 3x,Questions and 5x $ 54by . Find the value Indicator: of statement will always be true? 4 4 4x. !DBG # !EBG www.jmap.org 1 m!B 275" m!A In the diagram below, RST is a 3 ! 4 ! 5 right 279 Tri Whichstatement quadrilateral thattriangle alwaysis Which abouthas thediagonals of the 2 m!A180 & m!B triangle. The altitude, h, tosides the hypotenuse has ref mance Indicator: 158Topic The vertices of the triangle in the diagram below G.G.43: CENTROID bisect its angles and also bisect each other? true? 3 m!A " m!C been drawn. Determine the length of h. ofIn 198 In th 185 rhombus are A(7,9), B(3,3) , and C(11,3). 11 AB ! AC ! BC 4 m!C ' m!B 121 In right DEF , m!D " 90 and m!F is 12 degrees BC cm. 2 AB rectangle " AC and AC ! BC 160 In the diagram2of below, Jose found ABC less than twice . coordinates Find m!E . M(1,1), m!E 194 Quadrilateral MATH has at of po parallelogram 33 AC ! ABthe ! BC centroid P by constructing three medians. He 1 A(!2,5), T(3,5), and H(6,1) . Prove that isosceles trapezoid 44 AC # AB and ! BC 32 CF angles and found it toisosceles be AB 6 inches. 125 measured If the vertex of two triangles are 2 quadrilateral MATH is a rhombus and prove that it by Performance Geometry Regents Exam Questions Indicator: Topic congruent, then the triangles must be ogram 3 is not a square.www.jmap.org [The use of the grid is optional.] 1 acute181 The diagonals of a quadrilateral are congruent but D(3,4) . 4 do not bisect other.isThis quadrilateral is 2 congruent e 255 The volume of each a cylinder 12,566.4 cm3. The G.G.14: VOLUME AND LATERAL AREA 1 an trapezoid 3 right height le? ofisosceles the cylinder is 8 cm. Find the radius of 2 cylinder a parallelogram 252 Which expression represents the volume, in cubic4 similar the to the nearest tenth of a centimeter. 3 a rectangle centimeters, of the cylinder represented in the 4 a rhombus diagram below? 256 AG.G.54: right circular cylinder has an altitude of 11 feet REFLECTIONS If PF ! x , which can be used to isfind andequation a radius of 5 feet. What the x? lateral area, in 1 x " x ! 6 square feet, of the cylinder, to the nearest tenth? 276 Point A is located at . The point is reflected (4,!7) 25 2 2x " x ! 61 172.7 Wha in the x-axis. Its image is located at What are the coordinates of the centroid of A(!5,6), 3 3x " 2x ! 261 172.8 1 (!4,7) ABC ? 3 345.4 2 2 (!4,!7) 4 x " x ! 462 345.6 1 (5,6) 3 gram but 3 3 (4,7) 2 (7,3) 4 use of 280 Tri 4 (7,!4) 37 3 (7,5) C(4 G.G.15: VOLUME AND LATERAL AREA 4 (9,6) 161 In the diagram below of ABC , medians AD, BE , A 277 In What is the image of the point afterhas thea (2,!3)cone tra at G. and CF intersect 257 the diagram below, a right circular diameter of 8 inches transformation ? a height of 12 inches. r y ! axisand opt 159 Triangle ABC has vertices A(3,3), B(7,9) , and 1 (2,3) C(11,3). Determine the point of intersection of the 2 (!2,!3) 195 Given: with 1its vertices , B(2,8) andthe A(!6,!2)[The medians, ABC and state coordinates. use, of 162! 40 3 (!2,3) AB BC . has midpoint D, has midpoint E, C(6,!2) 324! set of axes below is2optional.] 4 (!3,2) and AC has midpoint3F. 972! 4 3,888! Prove: ADEF is a parallelogram ADEF is not a rhombus 278 The coordinates of point A are (!3a,4b). If point [The use of the grid is optional.] FG ?A reflected over the line is the the image lengthofofpoint A' is 253 What is the volume, in cubic centimeters, of a If CF ! 24, what 1 8 , the coordinates of A' are y " x cylinder that has a height of 15 cm and a diameter 2 10 of 12 cm? 1 (4b,!3a) 3 12 1 180! 2 (3a,4b) 4 16 2 540! 3 (!3a,!4b) What is the volume of the cone to the nearest cubic 3 675! inch? 4 (!4b,!3a) 4 2,160! 1 201 2 481 3 603 254 A right circular cylinder has a volume of 1,000 4 804 cubic inches and a height of 8 inches. What is the radius of the cylinder to the nearest tenth of an inch? 258 A right circular cone has a base with a radius of 15 1 6.3 cm, a vertical height of 20 cm, and a slant height of 2 11.2 25 cm. Find, in terms of' ! , the number of square 3 19.8 centimeters in the lateral area of the cone. 57 4 39.8
TRANSFORMATIONS
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Geo Regents Review 6.docx
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O from an re drawn. "AOB?
x2 ! y2 " 8 x 2 ! y 2 " 16
237 Write diagr
G.G.51: ARCS DETERMINED BY ANGLES 235 What is an equation of circle O shown in the graph below?
211 In the diagram below of circle O, chords AD and BC intersect at E.
A. Which oints A, B,
Which relationship must be true? 1 CAE # DBE mance Indicator: Topic 2 AEC $ BED 3 "ACB # "CBD
1 2 3
4 CA #TANGENTS DB G.G.50:
D is
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(x ! 1) 2 ! (y # 3) 2 (x # 1) 2 ! (y ! 3) 2 (x # 5) 2 ! (y ! 6) 2 (x ! 5) 2 ! (y # 6) 2
" 25 " 25 " 25 " 25
205 In the diagram below, circle A and circle B are shown.
Geometry Regents Exam Questions by Performance Indicator: Topi 49 www.jmap.org
Geometry Regents Exam Questions by Performance Indicator: Topic
Geometry Questions 267 As Regents shown in Exam the diagram below,by Performance , 269 Top In ABC ! DEFIndicator:
www.jmap.org
www.jmap.org AB " 7x, BC " 4, DE " 7, and EF " x . G.G.53: SEGMENTS INTERCEPTED BY CIRCLE G.G.16: VOLUME AND SURFACE AREA
216 In the diagram below of circle C, mQT ! 140, and m"P ! 40. 43
AB len 264 A rec len rat
218 In the diagram below, a tangentintocubic circlecentimeters, O at 259 PS Theisvolume, of a sphere whose 6 centimeters is point S, PQR is a secant, PS ! diameter x , PQ ! 3is, and 1 12! PR ! x # 18.
2 3 4
What is the total number of lines of tangency that are common to circle A and circle B? 1 1 2 2 3 3 What is mRS ? 4 4
ith bases diameter
1
36! 48! 288!
2 3
260 If the surface area of a sphere is represented by the volume 144 ! , what What is theislength of AB?in terms of ! ? 11 36 ! 28 22 48 2! 33 216 14 ! 44 288 4 !
1 50 2 60 206 3How90many common tangent lines can be drawn to 4 110
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G.G
265 In Gi 270 sta BC res 1 hyp
the two externally tangent circles shown below?
261 has a diameter 18 meters. the , 268 AInsphere the diagram below, of ABC ! EFGFind volume of the sphere, in cubic meters, in terms of m#C " 4x $ 30, and m#G " 5x $ 10 . Determine What is the length of PS!the ?. value of x.
217 In the diagram below, tangent ML and secant MNK are drawn to circle O. The ratio
1 2 3 4
mLN : mNK : mKL is 3:4:5. Find m"LMK .
1 2 3 4
1 2 3 4
6 9 3 27
2 3
262 Tim is going to paint a wooden sphere that has a diameter of 12 inches. Find the surface area of the sphere, to the nearest square inch.
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266 If Wh wh cen 1 12 23 3 4 4
G.G.45: SIMILARITY 263 Two triangles are similar, and the ratio of each pair of corresponding sides is 2:1. Which statement regarding the two triangles is not true? 1 Their areas have a ratio of 4:1. 2 Their altitudes have a ratio of 2:1. 3 Their perimeters have a ratio of 2:1. 4 Their corresponding angles have a ratio of 2:1.
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Geo Regents Review 6.docx
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4 Ms. Menard Name: _________________ 3 Geometry Regents Exam Questions by Performance Indicator: Topic 3 MG22G 4www.jmap.org Regents Review #6 due date ___________ 4 # 3 48 In circle O, a diameter has endpoints (!5,4) and G.G.1: PLANES Show all work even for multiple choice questions. This will be graded and counted as a quiz! (3,!6). What is the length of the diameter? 53 Lines k 1 and k 2 intersect at point E. Line m is 1 of a2 line that is perpendicular to 6 What is the slope perpendicular to lines k 1 and k 2 at point E. the line whose2 equation 2 2 is 3x " 5y ! 4? 3 10 3 1 # mance the lineIndicator: Topic 5 4 2 41 3 2 5 line 1 5 What is the of the line y #segment x " 4 whose 13 3The #lines49represented bylength the equations 2 ? 3 endpoints are A(!1,9) and B(7,4) and 3x 5 # 6y " 12 are 4 61 1 1 3the same line 2 89 2 parallel LAR 205 3 3 perpendicular 7 What is the slope of anor line that is perpendicular to 4 neither parallel 4 233theperpendicular mance Indicator: Topic the line represented by equation x " 2y ! 3? ular to 1 #2 2The 2is and 2yofsystem are 14 What lines 3y # 1 "of6x # following 4length # the 1 " line xof! 9segment What isthe the whose 34 the50 solution x 1 1 parallel equations? endpoints are and ? (1,!4) (9,2) 3 # 2 Which statement is always true? 2 perpendicular 1 y !5 (x # 3) 2 " 4 1 1 Lines k 1 and k 2 are perpendicular. 3 the same line 4 2 y !2 2x 17 #5 2 neither parallel 2 Line m is parallel to the plane determined by 3 10 nor perpendicular 14 (0,"4) lines k 1 and k 2 . 2 ("4,0) 4 2 26 3 Line m is perpendicular to the plane 3 ("4,"3) and (0,5) l to the 1 determined by lines k 1 and k 2 . 4The("3,"4) and of (5,0) 15 equation line k is . The equation y " x ! 2 Geometry Exam by by Indicator: Performance 1 Geometry 3Questions RegentsRegents Exam Questions Performance Topic Indicator: Topic 51 What is the length, to the nearest tenth, of the line 4 Line m is coplanar with lines k 1 and k 2 . www.jmap.org www.jmap.org of line m is !2x # 6y " 18. Lines k and m are segment joining the points (!4,2) and (146,52)? 35 Solve the following system of equations 1 parallel 1 a compass 141.4 82 graphically. The diagram below shows theand construction of the construct 84 the One step in a construction uses CONSTRUCTIONS the endpoints of AB Using straightedge, G.G.18: 2 79perpendicular f 2bisector !, lines and n intersect at point A. If 54 the In same planeradii. 2150.5 toall create arcs with Them arcs AB. perpendicular of 2x " 4x ! y # 1 angle bisector of shown below. [Leave !ABC 3 the same3line151.9 intersect above and below the segment. Whattoisline m and line n at point line k is perpendicular 81 Which diagram shows the construction of the construction 4 neither parallel x #nor ymarks.] ! perpendicular 1 4 158.1 the relationship of AB linek connecting the A, and thentheline is of AB? points of intersection1perpendicular of these arcs? inbisector contained plane ! the line 1 collinear 2 parallel to plane ! 16 The two lines represented by the equations below 2 . congruent 52 The endpoints of PQ are P(!3,1) and Q(4,25) are graphed on a coordinate plane. 3 parallel 3 perpendicular to plane ! Find thex length # 6y "of 12PQ . 4 perpendicular 4 skew to plane ! 3(x ! 2) " !y ! 4 85 On the diagram of ABC shown below, use a Which statement best describes the two lines? compass and straightedge to construct the 1 The lines are parallel. iven perpendicular bisector of AC . [Leave all 2 The lines are the same line. construction marks.] 3 The lines are perpendicular. 1 4 The lines intersect at an angle other than 90°. e of m Which statement is not true? 1 AC ! CB 1 2 CB ! AB 80 On2the diagram below, use a compass and 3 AC ! 2AB straightedge to construct the bisector of !ABC . 4 AC " CB ! AB
tion to
[Leave all construction marks.]
83 Line segment AB is shown in the diagram below.
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5
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Which two sets of construction marks, labeled I, II, III, and IV, are part of the construction of the perpendicular bisector of line segment AB? 1 I and II 2 I and III 3 II and III 4 II and IV
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2 3 4
120° 90° 60°
1 2
The intersection of the angle bisectors of a 248 A prism has volume of AC and BD 182 G triangle is the of the circumscribed 178center Inrectangular rhombus ABCD, thea diagonals 2 3x ! 18x !at24E.. Its a length x ,!what 2 andisa the re circle. intersect If base AE !has 5 and BE !of12 width of 3. Which expression represents the height m 3 The intersection of the perpendicular bisectors length of AB? of the prism? 1 of the sides of a triangle is the center of the 1 7 1 x!4 2 inscribed circle. 2 10 2 x!2 3 4 The intersection of the perpendicular bisectors Geometry Exam Questions by Performance Indicator: Topic 33 Regents 313 4 of the sides of a triangle 2 is the center of the 4 17 www.jmap.org 4 x ! 6x ! 8 circumscribed circle. What is the measure of !A? 197 In th 1 40° 179 CONICS G In the diagram below, quadrilateral STAR is a and 2 50° G.G.49: CHORDS rhombus with diagonals SA and TR intersecting at 183chor If 3 70° E. ST ! 3x " 30, SR ! 8x # 5, SE ! 3z, TE ! 5z " 5, ea the diagram below, ABC is inscribed in circle 4 100°196 InAE ! 4z # 8, m$RTA ! 5y # 2, and 1 P. The distances from the center of circle P to each Find SR, RT, and m$TAS . 52 m$TAS 9y " 8 . are 2 side of the!triangle shown. 3 123 In ABC , AB % BC . An altitude is drawn from B 4
117 In ABC , m!A " x , m!B " 2x # 2 , and What is the value of the x? m!C " 3x # 4 . represents This construction how to find 1 29 of intersection 31angle bisectors of ABC 12 the 59medians to the sides of ABC 23 the 34 the 61altitudes to the sides of ABC 4
1 20 of 6 cm 2 60 3 120 the heig Geometry Regents Exam Questions by Performance Indicator: Top The intersection of angle bisectors of a 4 the 240 triangle is www.jmap.org the center of the inscribed circle.
the perpendicular bisectors of the sides of ABC
118 In DEF , m!D " 3x # 5 , m!E " 4x $ 15 , and m!F " 2x # 10 . Which statement is true? 156 In1 the DF diagram " FEbelow of ABC , CD is the bisector AEFE , is the bisector of !CAB, and BG is of2 !BCA DE " drawn. 3 m!E " m!F 4 m!D " m!F
to AC and intersects AC at D. Which conclusion is not always true? 1 !ABD % !CBD 2 !BDA % !BDC 3 AD % BD 4 AD % DC
119 Triangle PQR has angles in the ratio of 2:3:5. Which type of triangle is PQR? 1 acute 2 isosceles 3 obtuse 4 right
184 Is BD va 1 Wha Which statement must be true? 2 1 1 DG " EG Geometry Regents Exam Questions by Performance Indicator: Topi 23 " BGmeasures of the angles of ABC are 120 2TheAG degree 124 In isosceles triangle ABC, AB " BC . Which www.jmap.org 3 3represented !AEB # !AEC Geometry Regents Exam Performance Topic by x, 3x,Questions and 5x $ 54by . Find the value Indicator: of statement will always be true? 4 4 4x. !DBG # !EBG www.jmap.org 1 m!B 275" m!A In the diagram below, RST is a 3 ! 4 ! 5 right 279 Tri Whichstatement quadrilateral thattriangle alwaysis Which abouthas thediagonals of the 2 m!A180 & m!B triangle. The altitude, h, tosides the hypotenuse has ref mance Indicator: 158Topic The vertices of the triangle in the diagram below G.G.43: CENTROID bisect its angles and also bisect each other? true? 3 m!A " m!C been drawn. Determine the length of h. ofIn 198 In th 185 rhombus are A(7,9), B(3,3) , and C(11,3). 11 AB ! AC ! BC 4 m!C ' m!B 121 In right DEF , m!D " 90 and m!F is 12 degrees BC cm. 2 AB rectangle " AC and AC ! BC 160 In the diagram2of below, Jose found ABC less than twice . coordinates Find m!E . M(1,1), m!E 194 Quadrilateral MATH has at of po parallelogram 33 AC ! ABthe ! BC centroid P by constructing three medians. He 1 A(!2,5), T(3,5), and H(6,1) . Prove that isosceles trapezoid 44 AC # AB and ! BC 32 CF angles and found it toisosceles be AB 6 inches. 125 measured If the vertex of two triangles are 2 quadrilateral MATH is a rhombus and prove that it by Performance Geometry Regents Exam Questions Indicator: Topic congruent, then the triangles must be ogram 3 is not a square.www.jmap.org [The use of the grid is optional.] 1 acute181 The diagonals of a quadrilateral are congruent but D(3,4) . 4 do not bisect other.isThis quadrilateral is 2 congruent e 255 The volume of each a cylinder 12,566.4 cm3. The G.G.14: VOLUME AND LATERAL AREA 1 an trapezoid 3 right height le? ofisosceles the cylinder is 8 cm. Find the radius of 2 cylinder a parallelogram 252 Which expression represents the volume, in cubic4 similar the to the nearest tenth of a centimeter. 3 a rectangle centimeters, of the cylinder represented in the 4 a rhombus diagram below? 256 AG.G.54: right circular cylinder has an altitude of 11 feet REFLECTIONS If PF ! x , which can be used to isfind andequation a radius of 5 feet. What the x? lateral area, in 1 x " x ! 6 square feet, of the cylinder, to the nearest tenth? 276 Point A is located at . The point is reflected (4,!7) 25 2 2x " x ! 61 172.7 Wha in the x-axis. Its image is located at What are the coordinates of the centroid of A(!5,6), 3 3x " 2x ! 261 172.8 1 (!4,7) ABC ? 3 345.4 2 2 (!4,!7) 4 x " x ! 462 345.6 1 (5,6) 3 gram but 3 3 (4,7) 2 (7,3) 4 use of 280 Tri 4 (7,!4) 37 3 (7,5) C(4 G.G.15: VOLUME AND LATERAL AREA 4 (9,6) 161 In the diagram below of ABC , medians AD, BE , A 277 In What is the image of the point afterhas thea (2,!3)cone tra at G. and CF intersect 257 the diagram below, a right circular diameter of 8 inches transformation ? a height of 12 inches. r y ! axisand opt 159 Triangle ABC has vertices A(3,3), B(7,9) , and 1 (2,3) C(11,3). Determine the point of intersection of the 2 (!2,!3) 195 Given: with 1its vertices , B(2,8) andthe A(!6,!2)[The medians, ABC and state coordinates. use, of 162! 40 3 (!2,3) AB BC . has midpoint D, has midpoint E, C(6,!2) 324! set of axes below is2optional.] 4 (!3,2) and AC has midpoint3F. 972! 4 3,888! Prove: ADEF is a parallelogram ADEF is not a rhombus 278 The coordinates of point A are (!3a,4b). If point [The use of the grid is optional.] FG ?A reflected over the line is the the image lengthofofpoint A' is 253 What is the volume, in cubic centimeters, of a If CF ! 24, what 1 8 , the coordinates of A' are y " x cylinder that has a height of 15 cm and a diameter 2 10 of 12 cm? 1 (4b,!3a) 3 12 1 180! 2 (3a,4b) 4 16 2 540! 3 (!3a,!4b) What is the volume of the cone to the nearest cubic 3 675! inch? 4 (!4b,!3a) 4 2,160! 1 201 2 481 3 603 254 A right circular cylinder has a volume of 1,000 4 804 cubic inches and a height of 8 inches. What is the radius of the cylinder to the nearest tenth of an inch? 258 A right circular cone has a base with a radius of 15 1 6.3 cm, a vertical height of 20 cm, and a slant height of 2 11.2 25 cm. Find, in terms of' ! , the number of square 3 19.8 centimeters in the lateral area of the cone. 57 4 39.8
TRANSFORMATIONS
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53
Geo Regents Review 6.docx
4
24
3 4
O from an re drawn. "AOB?
x2 ! y2 " 8 x 2 ! y 2 " 16
237 Write diagr
G.G.51: ARCS DETERMINED BY ANGLES 235 What is an equation of circle O shown in the graph below?
211 In the diagram below of circle O, chords AD and BC intersect at E.
A. Which oints A, B,
Which relationship must be true? 1 CAE # DBE mance Indicator: Topic 2 AEC $ BED 3 "ACB # "CBD
1 2 3
4 CA #TANGENTS DB G.G.50:
D is
4
(x ! 1) 2 ! (y # 3) 2 (x # 1) 2 ! (y ! 3) 2 (x # 5) 2 ! (y ! 6) 2 (x ! 5) 2 ! (y # 6) 2
" 25 " 25 " 25 " 25
205 In the diagram below, circle A and circle B are shown.
Geometry Regents Exam Questions by Performance Indicator: Topi 49 www.jmap.org
Geometry Regents Exam Questions by Performance Indicator: Topic
Geometry Questions 267 As Regents shown in Exam the diagram below,by Performance , 269 Top In ABC ! DEFIndicator:
www.jmap.org
www.jmap.org AB " 7x, BC " 4, DE " 7, and EF " x . G.G.53: SEGMENTS INTERCEPTED BY CIRCLE G.G.16: VOLUME AND SURFACE AREA
216 In the diagram below of circle C, mQT ! 140, and m"P ! 40. 43
AB len 264 A rec len rat
218 In the diagram below, a tangentintocubic circlecentimeters, O at 259 PS Theisvolume, of a sphere whose 6 centimeters is point S, PQR is a secant, PS ! diameter x , PQ ! 3is, and 1 12! PR ! x # 18.
2 3 4
What is the total number of lines of tangency that are common to circle A and circle B? 1 1 2 2 3 3 What is mRS ? 4 4
ith bases diameter
1
36! 48! 288!
2 3
260 If the surface area of a sphere is represented by the volume 144 ! , what What is theislength of AB?in terms of ! ? 11 36 ! 28 22 48 2! 33 216 14 ! 44 288 4 !
1 50 2 60 206 3How90many common tangent lines can be drawn to 4 110
4
G.G
265 In Gi 270 sta BC res 1 hyp
the two externally tangent circles shown below?
261 has a diameter 18 meters. the , 268 AInsphere the diagram below, of ABC ! EFGFind volume of the sphere, in cubic meters, in terms of m#C " 4x $ 30, and m#G " 5x $ 10 . Determine What is the length of PS!the ?. value of x.
217 In the diagram below, tangent ML and secant MNK are drawn to circle O. The ratio
1 2 3 4
mLN : mNK : mKL is 3:4:5. Find m"LMK .
1 2 3 4
1 2 3 4
6 9 3 27
2 3
262 Tim is going to paint a wooden sphere that has a diameter of 12 inches. Find the surface area of the sphere, to the nearest square inch.
4
266 If Wh wh cen 1 12 23 3 4 4
G.G.45: SIMILARITY 263 Two triangles are similar, and the ratio of each pair of corresponding sides is 2:1. Which statement regarding the two triangles is not true? 1 Their areas have a ratio of 4:1. 2 Their altitudes have a ratio of 2:1. 3 Their perimeters have a ratio of 2:1. 4 Their corresponding angles have a ratio of 2:1.
42
45
55
54
Geo Regents Review 6.docx
