Name:________________________
Name:________________________ Per:__________ Date:___________________
Geometry
Chapter 6 Test A
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 [pic] and [pic] find [pic] The diagram is not to scale.
[pic]
|a. |9 |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.
[pic]
|a. |x = 10, y = 38 |b. |x = 10, y = 21 |c. |x = 10, y = 7 |d. |x = 7, y = 10 |
____ 4. If [pic] [pic] [pic] and [pic] find the values of x and y for which LMNO must be a parallelogram. The diagram is not to scale.
[pic]
|a. |x = 4, y = [pic] |c. |x = 11, y = [pic] |
|b. |x = 4, y = [pic] |d. |x = 11, y = [pic] |
____ 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.
[pic]
|a. |[pic] [pic] |c. |[pic] [pic] |
|b. |[pic] [pic] |d. |[pic] [pic] |
____ 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.
[pic]
|a. |67°; 134° |b. |67°; 113° |c. |46°; 134° |d. |46°; 113° |
____ 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. [pic] are base angles of isosceles trapezoid JKLM. If [pic] and [pic](Draw a picture)
|a. |151 |b. |1 |c. |29 |d. |75.5 |
____ 10. In quadrilateral MNOP, [pic] Which of a parallelogram, trapezoid, or rhombus could quadrilateral MNOP be? (Draw a picture)
|a. |parallelogram or rhombus |c. |trapezoid only |
|b. |parallelogram only |d. |any of the three |
Short Answer
11. Isosceles trapezoid ABCD has legs [pic] and [pic] and base [pic] If AB = 4y – 3, BC = 3y – 4, and CD = 5y – 10, find the value of y. (Draw a picture)
12. Give the name that best describes the parallelogram and find the measures of the numbered angles. The diagram is not to scale.
[pic]
13. Find the values of the variables and the lengths of the sides of this rectangle. The diagram is not to scale.
[pic]
14. Complete this statement: For parallelogram ABCD, [pic]
Then state a definition or theorem that justifies your answer.
[pic]
15. Find the values of the variables and the lengths of the sides of this kite.
[pic]
16. ABCD is a parallelogram. If [pic] then [pic] The diagram is not to scale.
[pic]
17. Find the values of the variables in the parallelogram. The diagram is not to scale.
[pic]
18. Find [pic] in the kite. The diagram is not to scale.
[pic]
19. [pic] and [pic] Find [pic] The diagram is not to scale.
[pic]
20. ABCD is a parallelogram. If [pic] then [pic] The diagram is not to scale.
[pic]
21. Find AM in the parallelogram if PN =9 and AO = 4. The diagram is not to scale.
[pic]
Find the coordinates of the midpoint of the segment with the given endpoints. P( 10, -1) and Q( 7, 3)
23. In the rhombus, [pic] Find the value of each variable. The diagram is not to scale.
[pic]
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.
25. Find the length of the segment. Simplify the radical!
EXTRA CREDIT
Use the given endpoint R and midpoint M of RS to find the coordinates of the other endpoint S. (1 point)
R( -3, 7), M( 2, -4)
27. Write a proof (3 points)
Given: [pic]
Prove: VX = XT, SX = XU
[pic]
-----------------------
Statements
Reasons
11. y = _______________
12. ___________________
[pic]__________
[pic]__________
[pic]__________
[pic]__________
13. y = _______________
x = _______________
length short side_________
length long side__________
x + 13
5y
5x
y + 31
14. [pic]_______________
_______________________
15. y = ________________
x = ________________
length long side__________
length short side_________
16.[pic]___________
17. x = ________________
y =_________________
z =_________________
18. [pic]______________
[pic]______________
19. [pic]=______________
20. [pic]_____________
21. [pic]_______________
22. ________________________
26. _______________________
23. y = ________________
x = ________________
z = _________________
24.
length short sides ______________
length long sides _______________
25. TR = _______________
................
................
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