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Total Score: ____/90
Quadrilaterals Review Worksheet
___/22 Part I – Quad Properties: Put an x in the box if the shape always has the given property.
Property
1. Both pairs of opp. sides are  .
2. Diagonals are  .
3. Diagonals are perpendicular.
4. Diagonals bisect one another.
5. Consecutive angles are suppl.
6. Both pairs of opp. s are  .
Parallelogram
Rectangle
X
X
X
x
X
X
Rhombus
X
X
X
X
X
X
x
x
Square
Isosceles Trapezoid
X
X
X
X
X
X
X
___/16 Part II – Name that Quad: List all the quadrilaterals that have the given property.
7. Both pairs of opposite sides are parallel.
a. _____parallelogram_____________
b. _____rectangle_____________
8. Both pairs of opposite sides are congruent.
a. ____ rectangle ______________
b. _____ square _____________
9. Both pairs of opposite angles are congruent.
a. ____ rectangle ______________
b. _____ square _____________
10. Exactly one pair of opposite sides is parallel
a. _____trapezoid_____________
c. ____rhombus______________
d. ____square______________
c. ____ rhombus ______________
d. _____ parallelogram _____________
c. ____ rhombus ______________
d. _____ parallelogram _____________
b. _____ isosceles trapezoid _____________
11. Exactly one pair of opposite sides is congruent.
a. _____ isosceles trapezoid _____________
12. Exactly one pair of opposite angles is congruent.
a. _____ kite _____________
__/6 Part III: Identify Quad
13. Provide all possible names for the quadrilaterals below.
a. trapezoid
b. square, rectangle, parallelogram, rhombus
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c. parallelogram
Form B
Kite
X
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__/15 Part IV: Parallelograms
14. If the following quadrilaterals are parallelograms, find the values of x, y and z.
a. z = 180 – 78 – 102; x = 29; y = 180 – 78-29 = 73
b. z = 105, x = 31, y = 44
15. Explain why it is impossible for each figure to be a parallelogram.
a. op sides not 
b. op angles not 
16. Given: ABCD is a parallelogram
BE  AD
Prove: 1  C
Statements
1. ABCD is a parallelogram
2. BE  AD
3. BC  AD
4. BE  BC
5. 1  C
Reasons
1. Given
2. Given
3. Op sides of parallelogram 
4. Transitive Prop
5. if sides then angles
__/6 Part V: Rectangles
Use rectangle ABCD and the given info to complete the following.
17. If AC = 4x – 60 and BD = 30 –x, find BD.
4x – 60 = 30 – x; 5x = 90; x = 18; BD = 12
18. If BAC = 4x + 5 and CAD = 5x – 14, find CAD.
4x + 5 + 5x – 14 = 90; 9x – 9 = 90; 9x = 99; x = 11;
CAD = 5(11) – 14 = 41
19. If DE = 13, find CE.
13
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Form B
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__/4 Part VI: Kite
Use kite ABCD and the given info to complete the following.
20. If AB = x + 3, BC = x + 4, CD = 2x -1 and AD = 3x –y, solve for
x and y
X + 3 = 3x – y; x + 4 = 2x - 1
X = 5, y = 7
21. If AEB = 5x – 10 and DE = 6x, find DB.
5x – 10 = 90; x = 20; DE = 120; DB = DE * 2 = 240.
__/6 Part VIII: Rhombus
Use rhombus ABCD and the given info to complete the following.
22. If ADB = 27, find ADC.
27 * 2 = 54
23. If DEC = 5x, find the value of x.
5x = 90; x = 18
24. If DE = 13, find DB.
13 * 2 = 26
__/6 Part IX: Squares
Use square ABCD and the given info to complete the following.
25. If BC = 3x + 14 and DC = 5x – 8, find the value of x.
5x – 8 = 3x + 14;2x = 22; x = 11
26. If AEB = 3x, find the value of x.
3x = 90; x = 30
27. If BAC = 5x, find the value of x.
5x = 45; x = 9
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Form B
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__/6 Part X: Trapezoid
ABCD is isosceles trapezoid with bases AB & CD and median EF. Use the given info to solve each problem.
28. If DC = 30 and AB = 42, find EF.
EF = ½ (30 + 42) = ½ (72) = 36
29. If A = 5x and D = 4x, find the value of x.
5x + 4x = 180; 9x = 180; x = 20
30. If EF = x + 5 and AB + CD = 4x + 6, find EF.
X + 5 = ½ (4x + 6) = 2x + 3 x = 2; EF = 2 + 5 = 7
__/3 Part XI: Coordinate Geometry
31. Determine what kind of quadrilateral PQRS is based on the following vertices. Justify your answer.
P(2,3), Q(5,9), R(11,6), S(8,0)
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
Parallelogram Test:
Slope PQ = 2; slope PS = -½; slope QR =- ½; Slope RS = 2
Opposite sides ||; parallelogram
Rectangle Test:
Slope PQ and PS are opposite reciprocals; Perpendicular sides; Rectangle
Rhombus Test:
Distance PQ = √45 and distance QR = √45
Consecutive sides congruent; rhombus
Square Test:
Both rectangle and rhombus; square
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Form B