Pre-AP Geometry Worksheet
Name: _______________________________
Section 6.3 - Conditions for Parallelograms
Period: ________
I.
Write out the reason which proves each quadrilateral is a parallelogram.
1.
2.
3.
20
100°
14
14
100°
20
II.
For what value of
x is the quadrilateral a parallelogram?
4.
5.
6.
x2+8x
3x+2
2x+27
5x-10
III.
(2x+40)°
Determine if each quadrilateral MUST be a parallelogram. Justify your answer. NOT drawn to scale!
7.
8.
9.
10.
11.
12.
117°
123°
123°
A) mY  mW  180
WX  ZY
78
78
102
Which statement below is not necessarily true?
13. Given: In quadrilateral WXYZ,
C)
102
57°
57°
63°
IV.
(3x+5)°
(5x-25)°
WZ and XY are congruent and parallel.
B)
X  Z
D)
WX ZY
V.
Error Analysis
14. 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
VI.
5
7
F
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.
15.
16.
8
8
VII.
Describe how to prove that quadrilateral
17.
18.
A
19.
A
B
A
B
D
D
D
C
B
C
C
VIII. Application.
20. In the diagram, ABCD is a parallelogram,
A
B
F
D
ABCD is a parallelogram.
E
C
BF  DE  12 , and CF  8 . Find AE . Explain your reasoning.