Name:________________________
Geometry
Chapter 6 Test A
Per:__________
Date:___________________
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which statement is true?
a. All quadrilaterals are rectangles.
b. All quadrilaterals are squares.
c. All rectangles are quadrilaterals.
d. All quadrilaterals are parallelograms.
____
2. For the parallelogram, if
3
find
The diagram is not to scale.
4
2
1
a. 9
____
and
b. 17
c. 173
d. 163
3. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to
scale.
A
B
4x – 2
y + 14
4y – 7
x + 28
D
C
a. x = 10, y = 38
____
b. x = 10, y = 21
c. x = 10, y = 7
4. If
and
be a parallelogram. The diagram is not to scale.
O
M
a. x = 4, y = 5
b.
find the values of x and y for which LMNO must
N
L
x = 4, y =
1
5
d. x = 7, y = 10
c.
1
5
d. x = 11, y = 5
x = 11, y =
____
5. DEFG is a rectangle. DF = 5x – 5 and EG = x + 11. Find the value of x and the length of each diagonal.
a. x = 4, DF = 13, EG = 13
c. x = 4, DF = 15, EG = 15
b. x = 4, DF = 15, EG = 18
d. x = 2, DF = 13, EG = 13
____
6. Find the values of a and b. The diagram is not to scale.
a°
113°
36°
b°
a.
b.
____
c.
d.
7. The isosceles trapezoid is part of an isosceles triangle with a 46° 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.
a. 67°; 134°
b. 67°; 113°
c. 46°; 134°
____
8. Which description does NOT guarantee that a trapezoid is isosceles?
a. congruent bases
b. congruent diagonals
c. both pairs of base angles congruent
d. congruent legs
____
9.
a. 151
are base angles of isosceles trapezoid JKLM. If
(Draw a picture)
b. 1
c. 29
d. 46°; 113°
and
d. 75.5
____ 10. In quadrilateral MNOP,
MNOP be? (Draw a picture)
a. parallelogram or rhombus
b. parallelogram only
Which of a parallelogram, trapezoid, or rhombus could quadrilateral
c. trapezoid only
d. any of the three
Short Answer
11. Isosceles trapezoid ABCD has legs
find the value of y. (Draw a picture)
and
and base
If AB = 4y – 3, BC = 3y – 4, and CD = 5y – 10,
11. y = _______________
12. Give the name that best describes the parallelogram and find the measures of the numbered angles. The
diagram is not to scale.
12. ___________________
|
m1  __________
4
3
|
|
m2  __________
m3  __________
1
2
 
m4  __________
|
13. Find the values of the variables and the lengths of the sides of this rectangle. The diagram is not to scale.
5x
13. y = _______________
x + 13
5y
x = _______________
length short side_________
y + 31
length long side__________
14. Complete this statement: For parallelogram ABCD,
Then state a definition or theorem that justifies your answer.
D
14. BO  _______________
C
_______________________
O
A
B
15. Find the values of the variables and the lengths of the sides of this kite.
y–2
|
x+ 2
15. y = ________________
|
2x + 2
length long side__________
||
||
x = ________________
length short side_________
x + 11
16. ABCD is a parallelogram. If
A
then
The diagram is not to scale.
B
16. mBCD  ___________
D
C
17. Find the values of the variables in the parallelogram. The diagram is not to scale.
29
17. x = ________________
102
y =_________________
z =_________________
y°
z°
x°
18. Find
in the kite. The diagram is not to scale.
18. m1  ______________
|
A
D
m3  ______________
|
1
2
B
||
||
3
39°
C
19.
and
Find
The diagram is not to scale.
19.
=______________
R
|
|
S
||
||
U
T
20. ABCD is a parallelogram. If
A
then
20. mBCD  _____________
B
D
The diagram is not to scale.
C
21. Find AM in the parallelogram if PN =9 and AO = 4. The diagram is not to scale.
M
N
21. AM  _______________
A
P
O
22. Find the coordinates of the midpoint of the segment with the given endpoints. P( 10, -1) and Q( 7, 3)
22. ________________________
In the rhombus,
not to scale.
Find the value of each variable. The diagram is
|
23.
|
23. y = ________________
3
x = ________________
1
|
|
2
z = _________________
24. One side of a kite is 8 cm less than four times the length of another side. The perimeter of the kite is 74 cm.
Find the lengths of the sides of the kite.
24.
length short sides ______________
length long sides _______________
25. Find the length of the segment. Simplify the radical!
25. TR = _______________
EXTRA CREDIT
26. Use the given endpoint R and midpoint M of RS to find the coordinates of the other endpoint S. (1 point)
26. _______________________
R( -3, 7), M( 2, -4)
27. Write a proof (3 points)
Given:
Prove: VX = XT, SX = XU
V
Statements
U
X
S
T
Reasons