Download Geometry Chap 8 Review

Name: ______________________
Class: _________________
Date: _________
Geometry Chap 8 Review
____
1. Consecutive angles in a parallelogram are always ________.
a. congruent angles
b. complementary angles
c. supplementary angles
d. vertical angles
____
2. Choose the statement that is NOT ALWAYS true.
For any parallelogram _______.
a. the diagonals bisect each other
b. opposite angles are congruent
c. the diagonals are perpendicular
d. opposite sides are congruent
True or False:
3. If a quadrilateral is a parallelogram, then consecutive angles are complementary.
4. If a quadrilateral is a parallelogram, then opposite angles are complementary.
5. AC
6.
ABCD is a parallelogram. Find the value of x
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ID: A
Name: ______________________
ID: A
7. Given: VU ≅ ST and SV ≅ TU
Prove: VX = XT
1. VU ≅ ST and SV ≅ TU
1. Given
2.
2. If both pairs of opp. sides of a quad.
are ≅ , then the quad. is a parallelogram.
3. VX = XT
3.
____
8. Which statement is true?
a. All quadrilaterals are squares.
b. All rectangles are squares.
c. All parallelograms are quadrilaterals.
d. All quadrilaterals are parallelograms.
____
9. Choose the statement that is NOT ALWAYS true. For a rhombus ________.
a. each diagonal bisects a pair of opposite angles
b. all four sides are congruent
c. the diagonals are congruent
d. the diagonals are perpendicular
____ 10. Which statement is NOT always true of a rhombus?
a. The diagonals are perpendicular to each other.
b. The diagonals bisect each other.
c. Each diagonal is longer than at least one side.
d. The sum of the diagonals is less than the perimeter.
11. If the diagonals of a parallelogram are perpendicular, then the parallelogram is also what type of figure?
12. True or false: A rectangle is a parallelogram.
13. True or false: A square is a rectangle.
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Name: ______________________
ID: A
14. True or false: Opposite angles in a parallelogram are supplementary.
Decide if the argument is valid or invalid. Explain your reasoning.
15. If a figure is a rhombus, then it is a parallelogram.
A square is a rhombus.
Therefore, a square is a parallelogram.
16. a. Is the statement "If a quadrilateral is a rectangle, then it is a parallelogram" True or False?
b. Write the inverse of the statement in part (a) and tell if it is True or False.
____ 17. Isosceles trapezoid JKLM has legs JK and LM, and base KL. If JK =8x − 9, KL =7x + 10, and LM =10x + 2,
find the value of x.
a. −1
c. 19
11
8
b. −
d.
2
3
18. Given: Trapezoid ABCD with midsegment EF. If EF = 23 and DC = 26, find the length of AB.
19. One side of a kite is 5 cm less than 2 times the length of another. If the perimeter is 8 cm, find the
length of each side of the kite.
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Name: ______________________
ID: A
20. Find m∠T in the diagram, if m∠R = 130° and m∠S = 60°.
21.
Given: kite EFGH
Prove: ∠F ≅ ∠H
Starement
1) EFGH is a kite
2) EF≅EH and
GF ≅ GH
3) EG ≅ EG
4)
5)
Reasons
1) Given
2)
3) Reflexive property of congruence
4)
5) CPCTC
____ 22. Use slope or the Distance Formula to determine the most precise name for the figure: A(–1, –4),
B(1, –1), C(4, 1), D(2, –2).
a. kite
b. trapezoid
c. rhombus
d. square
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Name: ______________________
ID: A
____ 23. Which statement is false?
a. All rhombuses are kites.
b. All squares are rhombuses.
c. Every kite is a rectangle.
d. All squares are quadrilaterals.
____ 24. Which statement is false?
a. Some rhombuses are rectangles.
b. Every rhombus is a quadrilateral.
c. Every square is a parallelogram.
d. Every parallelogram is a rhombus.
____ 25. Which statement is false?
a. If a quadrilateral is a square, then it is not a kite.
b. Some parallelograms are rhombuses.
c. All parallelograms are quadrilaterals.
d. If a quadrilateral is a rectangle, then it is a kite.
26. Quadrilateral ABCD has vertices A ÊÁË −2, − 5 ˆ˜¯ , B ÊÁË 8, − 5 ˆ˜¯ , C ÊÁË 6, − 1 ˆ˜¯ , and D ÊÁË 0, − 1 ˆ˜¯ . What type of
quadrilateral is ABCD? Explain your reasoning.
5
ID: A
Geometry Chap 8 Review
Answer Section
1. ANS: C
2. ANS: C
3. ANS:
False
MSC: DOK 2
MSC: DOK 2
MSC: DOK 1
4. ANS:
False
MSC: DOK 1
5. ANS:
10
MSC: DOK 2
6. ANS:
The fact that ABCD is a parallelogram means that AB and CD are parallel. That leads to
m∠DCB = m∠EBC = 132°, because m∠DCB and m∠EBC are congruent alternate interior angles formed
by a transversal through parallel lines. Because of angle addition, m∠DCB = 51° + x°. Using substitution,
51° + x° = 132°, so x = 132 − 51 = 81.
MSC: DOK 2
7. ANS:
1. VU ≅ ST and SV ≅ TU
1. Given
2. STUV is a parallelogram.
2. If both pairs of opp. sides of a quad.
are ≅ , then the quad. is a parallelogram.
3. VX = XT
3. T he diagonals of a
parallelogram bisect each other.
8.
9.
10.
11.
MSC: DOK 2
ANS: C
ANS: C
ANS: C
ANS:
A rhombus
MSC: DOK 1
MSC: DOK 2
MSC: DOK 2
MSC: DOK 2
1
ID: A
12. ANS:
True
MSC: DOK 1
13. ANS:
True
MSC: DOK 1
14. ANS:
False
MSC: DOK 1
15. ANS:
valid; Law of Syllogism
MSC: DOK 3
16. ANS:
a. True
b. If a quadrilateral is not a rectangle, then it is not a parallelogram. False
MSC: DOK 2
17. ANS: B
18. ANS:
20
MSC: DOK 2
MSC: DOK 2
19. ANS:
3 cm, 1 cm
MSC: DOK 2
20. ANS:
110°
MSC: DOK 2
21. ANS:
Sample answer: Since it is given that EFGH is a kite, then EF ≅ EH and GF ≅ GH because a kite has two
pairs of congruent adjacent sides. Also, EG ≅ EG by the Reflexive Property. So, by the SSS Postulate,
ΔEFG ≅ ΔEHG. Therefore, by the definition of congruent triangles, ∠F ≅ ∠H.
22.
23.
24.
25.
MSC:
ANS:
ANS:
ANS:
ANS:
DOK 2
C
C
D
D
MSC:
MSC:
MSC:
MSC:
DOK
DOK
DOK
DOK
2
1
1
1
2
ID: A
26. ANS:
An isosceles trapezoid; the figure has two parallel sides of unequal length with the other two sides being of
the same length.
MSC: DOK 2
3