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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
3. Tests for Parallelograms
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Exercise 25 Page 501

If both pairs of opposite angles are congruent, then the quadrilateral is a parallelogram.

Graph:

Is It a Parallelogram? No.

Practice makes perfect

Let's plot the given points and draw the quadrilateral on a coordinate plane. Then we can use the Distance Formula to determine whether it is a parallelogram.

A quadrilateral is a parallelogram if both pairs of opposite sides are congruent. Let's check if the sides are congruent.

Side Distance Formula Simplify
Length of JK: ( -4,- 4), ( - 3, 1) sqrt(( - 3-( -4))^2+( 1-( - 4))^2) sqrt(26)
Length of ML: ( 3, -3), ( 4, 3) sqrt(( 4- 3)^2+( 3-( -3))^2) sqrt(37)
Length of JM: ( -4, -4), ( 3, -3) sqrt(( 3-( -4))^2+( -3-( -4))^2) sqrt(50)
Length of KL: ( -3, 1), ( 4,3) sqrt(( 4-( -3))^2+( 3- 1)^2) sqrt(53)

Both pairs of opposite sides are not congruent. Therefore, it is not a parallelogram.

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Exercises 2 (Page 499)
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