Download Review Chapter 6 - Geometry A

Review Chapter 6 - Geometry A
Short Answer
1. Find the values of the variables and the lengths of the sides of this kite.
x +| 3
||
||
y–3
|
2x + 5
x+ 6
2. ABCD is a parallelogram. If
A
D
then
The diagram is not to scale.
B
C
3. LMNO is a parallelogram. If NM = x + 35 and OL = 4x + 8 find the value of x and then find NM and OL.
O
N
L
M
4. Find the values of the variables in the parallelogram. The diagram is not to scale.
5. In the parallelogram,
and
J
Find
The diagram is not to scale.
K
O
L
M
6. Find AM in the parallelogram if PN =14 and AO = 6. The diagram is not to scale.
M
N
A
P
7. If
O
find
so that quadrilateral ABCD is a parallelogram. The diagram is not to scale.
A
B
D
C
Find the value of each variable. The diagram
|
|
8. In the rhombus,
is not to scale.
3
1
|
|
2
9. DEFG is a rectangle. DF = 3x – 5 and EG = x + 3. Find the value of x and the length of each diagonal.
10. Find the values of a and b.The diagram is not to scale.
a°
48°
123°
b°
11. The isosceles trapezoid is part of an isosceles triangle with a 44° vertex angle. What is the measure of an
acute base angle of the trapezoid? Of an obtuse base angle? The diagram is not to scale.
12.
are base angles of isosceles trapezoid JKLM. If
13.
and
Find
The diagram is not to scale.
R
|
|
S
||
||
U
T
14. Find a counterexample to show that the conjecture is false.
Conjecture: Any number that is divisible by 2 is also divisible by 4.
15. Find the values of x and y. The diagram is not to scale.
(x – 1)°
53°
(y – 9)°
65°
and
16. The two triangles are congruent as suggested by their appearance. Find the value of d. The diagrams are not to
scale.
d°
43°
g
17
b
f°
e°
15
47°
8
c
17. Justify the last two steps of the proof.
Given:
and
Prove:
E
F
G
H
Proof:
1.
2.
3.
4.
1. Given
2. Given
3.
4.
18. Find the length of the midsegment. The diagram is not to scale.
33
42
6x + 5
42
33
3x + 46
19.
bisects
Find the value of x. The diagram is not to scale.
|
E
|
8x + 20
F
)
9x
)
21°
D
20.
G
Find
1
4
2
3
Drawing not to scale
21. Find the values of the variables and the lengths of the sides of this rectangle. The diagram is not to scale.
10x
2x + 8
10y
16y + 28
22. What type of quadrilateral has two pairs of parallel sides?
23. Isosceles trapezoid ABCD has legs
14, find the value of y.
and
and base
If AB = 5y – 3, BC = 3y – 3, and CD = 6y –
24. Give the name that best describes the parallelogram and find the measures of the numbered angles. The
diagram is not to scale.
|
4
|
|
3
1
2
100ο
|
25. Judging by appearance, classify the figure in as many ways as possible using rectangle, trapezoid, square,
quadrilateral, parallelogram, rhombus.
Review Chapter 6 - Geometry A
Answer Section
SHORT ANSWER
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
x = 1, y = 7; 4, 7
118
x = 9, NM = 44, OL = 44
104
6
134
x = 6, y = 84, z = 15
x = 4, DF = 7, EG = 7
68°; 112°
154
60
18
x = 66, y = 71
43
Reflexive Property of ; SSS
29
20
57
x = 6, y = 2; 20, 60
parallelogram
11
Rhombus; the measure of all numbered angles equal 42.
quadrilateral