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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

4. Rectangles

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Exercise 5 Page 508

The diagonals of a rectangle are congruent.

11

Practice makes perfect

Let's analyze the given quadrilateral to find the length EG. Keep the information that we have been provided in mind: we have been told that the figure is a rectangle, FD = 3x + 7, and EG = x + 5.

Recall the following theorem.

Rectangle Diagonals Theorem
The diagonals of a rectangle are congruent.

Therefore, their lengths are equal. FD=EG ⇔ 3x-7=x+5 We can use this equation to solve for x.

3x-7=x+5

▼

Solve for x

LHS-x=RHS-x

2x-7=5

LHS+7=RHS+7

2x=12

.LHS /2.=.RHS /2.

x=6

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

EG = x + 5

x= 6

EG = 6 + 5

Add terms

EG = 11

Subchapter links

Exercises p.508-511