Pre-AP Geometry Worksheet
Proving Parallelograms
I.
1.
Name___________________________
Write out what reason proves the following quadrilateral is a parallelogram.
2.
3.
20
100°
14
100°
14
20
II. For what value of x is the quadrilateral a parallelogram?
4.
5.
4x+2
x+7
2x+3
III.
7.
6.
6x
5x-6
Describe how to prove that ABCD is a parallelogram.
8.
A
D
9.
A
B
D
C
IV. Which statement below is not necessarily true?
10. In quadrilateral WXYZ, WZ and XY are congruent and parallel.
A) mY  mW  180
B) X  Z
C) WX  ZY
A
B
D
C
D) WX
3x+2
ZY
B
C
V. ERROR ANALYSIS
11. A student claims that because two pairs of sides are congruent, quadrilateral DEFG shown below
is a parallelogram. Explain the error that the student is making.
D
5
E
7
G
5
7
F
VI. For what value of x is the quadrilateral a parallelogram?
12.
13.
14.
66°
(x+10)°
x°
66°
(2x+20)°
x°
3x°
VII. Application
15. In the diagram, ABCD is a parallelogram, BF  DE  12 , and CF  8 . Find AE . Explain your
reasoning.
A
B
F
D
E
C
VIII. A student claims incorrectly that the marked information below can be used to show that the
figure is a parallelogram. Draw a quadrilateral with the marked properties that is clearly NOT a
parallelogram. Explain your reasoning.
16.
17.
8
8
IX. Proofs
18.
Given: A  C , B  D
Prove: ABCD is a parallelogram.
A
B
Hint: Let xo represent mA and mC . Let yo represent
mB and mD . Write and simplify and equation and solve.
D
C
19.
Given: Diagonals JL and KM bisect each other.
Prove: JKLM is a parallelogram.
K
L
P
Statements
Reasons
J
M