Download Int. Geometry Unit 8 Quiz (Lessons 1

Int. Geometry
Unit 8 Quiz (Lessons 1-5) Review
1
Questions 1-6: Quadrilateral KLMN is a parallelogram. Complete each statement.
M
N
6
4
5
3
X
7
8
1
K
2
L
1. KN ≅ _______
2. ∠NML ≅ ________
3. MX ≅ ______
4. ∠1 ≅ ________
5. ∠KNM is supplementary to ____________
6. ∆MLN ≅ ___________
Questions 7-12: If it is possible to prove a quadrilateral is parallelogram from the given
information, name the parallelogram. If it is not possible, write none.
Choose from FABE , FACD, BCDE , or none
7. FA ≅ EB; FA EB :__________________
8. FD ≅ AC ; AF ≅ CD :________________
E
F
4
9. FA EB; DC EB :__________________
D
3
G
10. ∠1 ≅ ∠3; ∠2 ≅ ∠4 :__________________
1
A
11. FD AC ; EB DC :_________________
12. FG ≅ GB; AG ≅ GE :________________
2
B
C
Int. Geometry
Unit 8 Quiz (Lessons 1-5) Review
2
13. The angles of a quadrilateral are in the ratio 3:10:7:4. What is the measure of the
smallest exterior angle?
14. Find the value of the missing angle.
D
27°
47°
A
165°
B
Questions 15-22: Decide whether you are given enough information to determine if a
quadrilateral is a parallelogram.
15. Opposite sides are parallel.
16. Opposite sides are congruent.
17. Two pairs of consecutive sides
are congruent.
18. Two pairs of consecutive angles
are congruent.
19. Diagonals are congruent.
20. Diagonals bisect each other.
21. All four sides are congruent.
22. Consecutive angles are supplementary.
Questions 23-24: Find the value of each variable in the parallelogram.
23.
24.
25.
26.
C
Int. Geometry
Unit 8 Quiz (Lessons 1-5) Review
3
27. Is it possible to have an exterior angle measure of 16.5 for a regular polygon?
Explain.
28. The measure of an interior angle of a regular polygon is 174. Name the polygon.
29. What is the measure of one interior angle for a regular hexagon?
30. The angles of a pentagon are 10 x , (12 x + 1) , ( 5 x + 6 ) , (11x + 16 ) , and 137 .
Find the measure of the smallest angle.
31. Find the measure of the marked angle. The polygons are regular polygons
x
32. Given: MN = AT; MATH is a parallelogram
M
A
Prove: ∠1 ≅ ∠2
1
2
H
33.
Given: ∠F ≅ ∠1 , EH ≅ FG; ∠1 ≅ ∠2
N
H
Prove: FGHI is a parallelogram
1
G
2
E
34.
T
What the interior and exterior angle measure of a 150-gon?
I
F
Int. Geometry
35.
Unit 8 Quiz (Lessons 1-5) Review
4
The angles of quadrilateral WXYZ are such that m∠W > m∠X > m∠Y > m∠Z .
The angles are in an arithmetic progression, meaning
m∠W − m∠X = m∠X − m∠Y = m∠Y − m∠Z . If m∠W is seven times the
measure of ∠Z , what is m ∠W ?
Answers:
1.
3.
5.
7.
9.
11.
13.
15.
17.
19.
21.
23.
25.
27.
28.
30.
ML
KX
∠NKL and ∠NML
FABE
None
BCDE
30
Yes
No
No
Yes
c = 6; d = 9
q = 8; p = 4
No, we would have 21.81 sides.
60-gon
56
2.
4.
6.
8.
10.
12.
14.
16.
18.
20.
22.
24.
26.
29.
31.
∠NKL
∠5
∆KNL
FACD
FABE
FABE
121°
Yes
No
Yes
Yes
g = 21; h = 8
t = 3; e = 8
120
117o
Note with the proofs, there are multiple solutions to these problems.
32. We know MATH is a parallelogram which means the opposite sides are congruent
so MH=AT.
We also know MN = AT, so by substitution MH = AT.
By the Isosceles Triangle Theorem ∠1 ≅ ∠2 .
33. We also know ∠1 ≅ ∠2 and ∠1 ≅ ∠F , so by transitivity ∠2 ≅ ∠F .
This means IH FG because corresponding angles are congruent.
Also since ∠1 ≅ ∠2 by the Isosceles Triangle Theorem EH ≅ HI . We know
EH ≅ FG so by transitivity IH ≅ FG .
There are now a pair of opposite sides that are congruent and parallel in FGHI
which means it is a parallelogram.
34. Interior = 177.6o
35. 144o
Exterior = 2.4o