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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

5. Conditions for Rhombuses, Rectangles, and Squares

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Exercise 13 Page 386

In a rectangle, the diagonals are congruent.

10

Practice makes perfect

We want to find the value of x for which the given figure is a rectangle. Theorem 6.18 tells us that if the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

This means that the lengths of the diagonals have to be equal. LN = MO We know that LN =4x - 7 and MO = 2x + 13. Let's substitute these values into above equation, and solve it for x.

LN = MO

LN= 4x - 7, MO= 2x + 13

4x - 7 = 2x + 13

LHS-2x=RHS-2x

2x - 7 = 13

LHS+7=RHS+7

2x = 20

.LHS /2.=.RHS /2.

x = 10

For x = 10 the given figure is a rectangle.

Subchapter links

Lesson Check p.386

Practice and Problem-Solving Exercises p.386-388

Standardized Test Prep p.388

Mixed Review p.388