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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Mid-Chapter Quiz

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Exercise 21 Page 504

Recall the theorem that states that if both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

x=8, y=7

Let's find the values for which the given quadrilateral is a parallelogram.

Recall the following theorem.

A quadrilateral is a parallelogram if both pairs of opposite sides are congruent.

Therefore, the lengths of the opposite sides of the given quadrilateral must be equal. Let's write an equation for each pair of opposite sides. 3x-2= 2x+6 and 6y-8= 4y+6 Let's solve the first equation to find x.

3x-2=2x+6

LHS-2x=RHS-2x

x-2 = 6

LHS+2=RHS+2

x = 8

Now, let's solve the second equation for y.

6y-8=4y+6

LHS-4y=RHS-4y

2y-8 = 6

LHS+8=RHS+8

2y = 14

.LHS /2.=.RHS /2.

y=7

Therefore, if x=8 and y=7, then the given quadrilateral is a parallelogram.