Advanced Geometry
Name:_______________________
Worksheet 6.3: Showing quadrilaterals are parallelograms
Determine whether each quadrilateral is a parallelogram. Explain your answer.
1.
2.
3.
o
118
o
62
4.
o
62
o
118
5.
6.
7. Use the slope formula to find the slope of each side of quadrilateral ROMY whose vertices
are R(-2,5), O(1,3), M(-3,-4), Y(-6,-2) respectively. Then determine if the quadrilateral is a
parallelogram. Remember m =
y 2 − y1
.
x 2 − x1
m RO = _____
mOM = _____
mMY = _____
m RY = _____
Is it a parallelogram? Yes or No
Find the value of x and y so that the quadrilateral is a parallelogram.
8.
(5x + 29)
(3y + 15)
10.
o
o
(5y – 9)
(7x – 11 )
o
9.
-4x – 2
-3x + 4
o
3y – 5
11.
-6x
2y + 8
(x + y)
(2x)
o
o
12y – 7
7y + 3
o
30
o
24
-4x + 6
12. Four jets are flying in formation. Three of the jets are shown in the graph.
a. If the 4 jets must be located at the vertices of a parallelogram,
what is a possible location for the 4th missing jet?
b. What is another location that the 4th missing jet could be
located at?
13. Aaron is making a wooden picture frame in the shape of a parallelogram. He has two
pieces of wood that are 3 feet long and two that are 4 feet long. If Aaron connects the
pieces of wood at their ends to each other, in what order must he connect them to make a
parallelogram?
Find the values to ensure that the quadrilateral is a parallelogram.
14. If m<MPO = 122°, then m<PON = ______ .
15. If m<PMN = 74°, then m<NOP = ______ .
16. If m<4 = 36°, then m< _____ = 36°.
17. If m<MNO = 106° and m<4 = 47°,
then m<3 = ______ ,.
18. If NR = 3x + 2 and RP = x + 14, then x = ______, NR = ______ and NP = ______ .
19. If MR = 2x + 4 and MO = 7x - 28, then x = ______, RO = ______ and MO = ______ .
20. If m<PMN = 8x - 5 and m<PON = 4x + 19, then x = ______, m<PMN = ______ and
m<MNO = ______ .
21. If m<MPO = 9x + 2 and m<PON = 5x + 10, then x = ______, m<MPO = ______,
m<PON = ______, and m<PMN = ______ .