1 Chapter 7 Study Guide Name: 1. Name the properties
Chapter 7 Study Guide
Name: ____________________
1. Name the properties of a parallelogram.
2. Name the properties of a rhombus.
3. Name the properties of a rectangle.
4. Name the properties of a square.
5. Name the properties of an isosceles trapezoid.
6. Name the properties of a kite.
1
Section 7.1: 7. Find the measure of the (a) SUM of the interior, (b), SUM of the exterior, (c) 1 interior angle of the regular polygon, and (d) 1 exterior angle of the regular polygon for the following polygons:
Dodecagon
Heptagon
25-agon
a.
a.
a.
b.
b.
b.
c.
c.
c.
d.
d.
d.
8. Find the values of ∠Y and ∠X.
9. Find the value of x.
10. Find the number of sides of the regular polygon if one of the interior angles is 1620?
Section 7.2:
11. Find the indicated measure in parallelogram MNQ. a. LM =
b. m∠LMN =
c. LP =
d. m∠NQL =
e. LQ =
f. m∠MNQ =
g. MQ =
h. m∠LMQ = 2
12. Find the coordinates of the intersection of the diagonals of the parallelogram with the vertices W(-2,5), X(2,5), Y(4,0), and Z(0,0).
13. Three vertices of parallelogram DEFG are D(0,2), E(-1,5), and G(4,0). Find the coordinates of the fourth vertex.
Section 7.3: 14. Find the values of x and y that make the quadrilateral a parallelogram.
15. Find the values of x and y that make the quadrilateral a parallelogram.
16. Quadrilateral JKLM has the coordinates J(-2,3), K(-5,7), L(3,6), and M(6,2). Name 5 different ways that you could prove that JKLM is a parallelogram. Be specific. a) b) c) d) e) Section 7.4 For any rectangle WXYZ, decide whether the statement is always, sometimes, or never true.
3
23. Quadrilateral DEFG is a rhombus, find the measure of the indicated angles. m∠1 = m∠4 = m∠2 = m∠5 = m∠3 = m∠6 =
24. Find the lengths of the diagonals of rectangle WXYZ when AE = 12x-4 and BD = -18x+13.
25. Name each quadrilateral – parallelogram, rectangle, rhombus, or square – for which the statement is always true. (Name it in as many ways as possible). a) It is equiangular. b) It is equiangular and equilateral. c) The diagonals are perpendicular. d) The diagonals bisect each other. e) The diagonals bisect the vertex angles. 26. The diagonals of rectangle QRST intersect at P. Given that m∠PTS = 340 and QS = 10, find the indicated measure. RT = m∠QTR = QP = m∠SRT = RP = m∠QRT =
Section 7.5: 27. Find AB.
28. Find the length of the midsegment of the trapezoid with the given vertices. A(2,0), B(8,-4), C(12,2), and D(0,10).
29. Find m∠G. 4
30. Give the most specific name for each quadrilateral a.
b.
c.
d.
31. Solve for x.
5
Name: ____________________
1. Name the properties of a parallelogram.
2. Name the properties of a rhombus.
3. Name the properties of a rectangle.
4. Name the properties of a square.
5. Name the properties of an isosceles trapezoid.
6. Name the properties of a kite.
1
Section 7.1: 7. Find the measure of the (a) SUM of the interior, (b), SUM of the exterior, (c) 1 interior angle of the regular polygon, and (d) 1 exterior angle of the regular polygon for the following polygons:
Dodecagon
Heptagon
25-agon
a.
a.
a.
b.
b.
b.
c.
c.
c.
d.
d.
d.
8. Find the values of ∠Y and ∠X.
9. Find the value of x.
10. Find the number of sides of the regular polygon if one of the interior angles is 1620?
Section 7.2:
11. Find the indicated measure in parallelogram MNQ. a. LM =
b. m∠LMN =
c. LP =
d. m∠NQL =
e. LQ =
f. m∠MNQ =
g. MQ =
h. m∠LMQ = 2
12. Find the coordinates of the intersection of the diagonals of the parallelogram with the vertices W(-2,5), X(2,5), Y(4,0), and Z(0,0).
13. Three vertices of parallelogram DEFG are D(0,2), E(-1,5), and G(4,0). Find the coordinates of the fourth vertex.
Section 7.3: 14. Find the values of x and y that make the quadrilateral a parallelogram.
15. Find the values of x and y that make the quadrilateral a parallelogram.
16. Quadrilateral JKLM has the coordinates J(-2,3), K(-5,7), L(3,6), and M(6,2). Name 5 different ways that you could prove that JKLM is a parallelogram. Be specific. a) b) c) d) e) Section 7.4 For any rectangle WXYZ, decide whether the statement is always, sometimes, or never true.
3
23. Quadrilateral DEFG is a rhombus, find the measure of the indicated angles. m∠1 = m∠4 = m∠2 = m∠5 = m∠3 = m∠6 =
24. Find the lengths of the diagonals of rectangle WXYZ when AE = 12x-4 and BD = -18x+13.
25. Name each quadrilateral – parallelogram, rectangle, rhombus, or square – for which the statement is always true. (Name it in as many ways as possible). a) It is equiangular. b) It is equiangular and equilateral. c) The diagonals are perpendicular. d) The diagonals bisect each other. e) The diagonals bisect the vertex angles. 26. The diagonals of rectangle QRST intersect at P. Given that m∠PTS = 340 and QS = 10, find the indicated measure. RT = m∠QTR = QP = m∠SRT = RP = m∠QRT =
Section 7.5: 27. Find AB.
28. Find the length of the midsegment of the trapezoid with the given vertices. A(2,0), B(8,-4), C(12,2), and D(0,10).
29. Find m∠G. 4
30. Give the most specific name for each quadrilateral a.
b.
c.
d.
31. Solve for x.
5
