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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Rectangles

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Exercise 14 Page 508

The opposite sides of a rectangle are congruent.

WX=5

Practice makes perfect

Let's analyze the given quadrilateral to find the length WX. Keep in mind that we have been told that the figure is a rectangle, that the segment ZY = 2x + 3, and that WX = x+ 4.

Since every rectangle is also a parallelogram, recall the following theorem.

Parallelogram Opposite Sides Theorem
The opposite sides in a parallelogram are congruent.

Therefore, the lengths of the segments ZY and WX are equal. ZY=WX ⇔ 2x+3=x+4 We can use this equation to solve for x.

2x+3=x+4

LHS-3=RHS-3

2x=x + 1

LHS-x=RHS-x

x = 1

Now that we know the value of x, we can find WX.

WX=x+4

x= 1

WX= 1+4

Add terms

WX=5

Subchapter links

Exercises p.508-511