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Name _______________________________________________ Date __________________ Block ______
1. Put an “x” in the box if the quadrilateral always has the given properties.
Property
Parallelogram
Both pairs of opp.
sides are ≅
Diagonals are ≅
X
Rectangle
Rhombus
Square
X
X
X
X
X
X
X
Diagonals are
perpendicular
Diagonals bisect
each other
Consecutive int.
angles are
supplementary
Both pairs of opp.
∠ are ≅
X
X
X
X
X
X
X
X
X
X
X
X
Isosceles
Trapezoid
Kite
X
X
X
Use rectangle ABCD to answer each question.
2. If m∠BAC = (4x + 5)˚ and m∠CAD = (5x – 14)˚,
find m∠CAD.
m∠CAD = 41˚
3.
If AC = 9x + 1 and BD = 13x – 11, find ED.
4. If m∠ADE = 68˚, find m∠AEB.
m∠AEB = 136˚
ED = 14
5. Determine if the quadrilateral is a parallelogram. If yes, tell why.
a)
Yes – the diagonals are
bisected.
b)
Yes – two pairs of opposite
angles are congruent.
Use kite ABCD to answer each question.
6. If AB = x + 3, BC = x + 4, CD = 2x - 1, and
AD = 3x - y, solve for x and y.
A
\
D
∕
E
B
C
x=
5
y=
7
7. If m∠AEB = (5x -10)˚ and DE = 3x, find DB.
8. Find AE if AB = 8√2 and BE = 6√2. Write your
answer in simplest radical form.
DB = 120
AE = 2√14
Use rhombus ABCD to answer each question.
9. If m∠ADB = 27˚, find m∠ADC.
C
D
E
A
m∠ADC = 27˚
B
10. If AE = 20 and DB = 26, find DC. Round your
answer to the nearest tenth.
DC = 23.9
11. Find the measure of angle ABC if
m∠ADB = (9x – 43)˚ and m∠CDB = (5x + 1)˚.
m∠ABC = 112˚
Use square ABCD to answer each question.
A
12. If AC = 32, find BC. Write your answer in
simplest radical form.
B
E
D
BC = 16√2
C
13. If m∠BAC = (9x)˚, find the value of x.
x=5
14. If m∠AEB = (5x – 10)˚, find the value of x.
x = 20
Use isosceles trapezoid ABCD, with AB and CD as bases and median EF to answer the following
questions.
15. If AB = 30 and DC = 42, find EF.
B
A
E
EF = 36
F
D
C
16. If m∠A = (5x)˚ and m∠D = (4x)˚, find the
value of x.
x = 20
18. What is the measure of each interior angle
of a regular 18-gon?
160˚
17. If EF = x + 5 and AB + CD = 4x + 6, find EF.
EF = 7
19. If the interior angle of a regular polygon is
162˚, how many sides does it have?
20 sides
20. If the sum of the interior angles of a polygon
is 3780˚, how many sides does it have?
21. Find the value of x.
x = 100
60˚
23 sides
x˚
x˚
x˚
22. Find the value of x.
23. Find the value of z.
x˚
110˚
80˚
(9z)ᵒ
42˚
(4z)ᵒ
x = 64
(5z + 25)ᵒ
2x˚
(5z – 10)ᵒ
z = 15
Complete the proof.
24.
B
Given: ABCD is a parallelogram
BE ≌ AD
Prove: ∠1 ≌ ∠C
C
Statement
A
1
E
D
Reason
1. ABCD is a parallelogram
1. Given
2. BE ≅ AD
2. Given
3. AD ≌ BC
3. Definition of a Parallelogram
4. BE ≌ BC
4. Transitive Property of Congruence
5. ∠1 ≅ ∠ C
5. Isosceles Triangle Theorem
(chapter 4 notes)