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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Rectangles

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Exercise 55 Page 511

Recall the theorem that says that a quadrilateral is a parallelogram if a pair of sides is both parallel and congruent.

x=8
y=22

Practice makes perfect

We want to find the values of x and y so that the quadrilateral is a parallelogram.

Value of x

Recall the theorem.

If a pair of sides of a quadrilateral is both parallel and congruent, then it is a parallelogram.

Therefore, we want the sides measuring 4x-17 and 2x-1 to have equal length. 4x-17= 2x-1 Let's solve this equation for x.

4x-17=2x-1

LHS+17=RHS+17

4x=2x+16

LHS-2x=RHS-2x

2x=16

.LHS /2.=.RHS /2.

x=8

Value of y

We also want these same sides to be parallel. Recall the theorem.

Converse Alternate Interior Angles Theorem
If a pair of alternate interior angles formed by a transversal are congruent, then the crossed lines are parallel.

Therefore, we want the angles measuring (3y+3)^(∘) and (4y-19)^(∘) to be congruent. (3y+3)= (4y-19) Let's solve it.

(3y+3)=(4y-19)

Remove parentheses

3y+3=4y-19

LHS-3y=RHS-3y

3=y-19

LHS+19=RHS+19

22=y

Rearrange equation

y=22

Subchapter links

Exercises p.508-511