Page 21 - Math Course 3 (Book 2)

Proving a Quadrilateral is a Parallelogram

Use Slope and Distance
Your Turn!

Example Find Measures

Find m so that the quadrilateral is a parallelogram.
COORDINATE GEOMETRY
Determine whether the figure with vertices 4m + 2
A(–3, 0), B(–1, 3), C(3, 2), and D(1, –1) is a
parallelogram. Use the Slope Formula.

3m + 8
B(–1, 3) A. m = 2
B. m = 3
C(3, 2) C. m = 6
A(–3, 0) D. m = 8

Answer
D(1, –1)
Use Slope and Distance
If the opposite sides of a quadrilateral are parallel, Determine whether the figure with the given vertices
then it is a parallelogram. is a parallelogram. Use the method indicated.

A(–1, –2), B(–3, 1), C(1, 2), D(3, –1); Slope Formula
3 – 0 3
Slope of AB = or
–1 – (–3) 2
–1 – 0 1
Slope of AD = or – 4 C(1, 2)
1 – (–3)
B(–3, 1)
–1 – 2 3
Slope of CD = or
1 – 3 2
3 – 2 1
Slope of BC = or –
–1 – 3 4
D(3, –1)
A(–1, –2)

Since opposite sides have the
same slope, AB || CD and AD || BC.
Answer
Therefore, ABCD is a A. yes
parallelogram by definition. B. no
C. cannot be determined

Answer

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