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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Study Guide and Review

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Exercise 31 Page 533

The diagonals of a rectangle are congruent.

64

Practice makes perfect

Let's analyze the given quadrilateral to find the length EG. Keep in mind that we have been told that the quadrilateral is a rectangle.

By the Segment Addition Postulate, we can express each diagonal as the sum of its smaller segments. Therefore, FH is the addition of FK and KH. FH= FK + KH Additionally, because a rectangle is a parallelogram, we know that the diagonals bisect each other. This means that FK and KH have the same length. FK=KH Let's use this information to find the length of FH. Recall that we know that FK=32.

FH= FK + KH

KH= FK

FH= FK + FK

Add terms

FH= 2FK

FK= 32

FH= 2( 32)

Multiply

FH=64

Now, recall that the diagonals of a rectangle are congruent. Therefore, their lengths are equal. FH = EG ⇔ EG = 64

Subchapter links

1 Angles of Polygons p.532

2 Parallelograms p.532

3 Tests for Parallelograms p.533

4 Rectangles p.533

5 Rhombi and Squares p.534

6 Trapezoids and Kites p.534