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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

7. Similarity Transformations

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Exercise 31 Page 600

If the parallelogram is rectangle, then its diagonals are congruent.

6

Practice makes perfect

We know that PQRS is a rectangle. There is a theorem that tells us that diagonals of a parallelogram bisect each other.

Lengths of the halves of the diagonal must be equal. 2x - 5 = 7-x Let's solve this equation to find x.

2x - 5 = 7 - x

LHS+x=RHS+x

3x - 5 = 7

LHS+5=RHS+5

3x = 12

.LHS /3.=.RHS /3.

x=4

To find QS, notice that diagonals of rectangle are congruent. QS ≅ PR By the definition of the congruent segments, lengths of QS and PR are equal. QS = (2x - 5) + (7 - x) Let's substitute x = 4 in above equation and simplify.

QS = (2x - 5) + (7 - x)

x= 4

QS = (2( 4) - 5) + (7 - 4)

Multiply

QS = (8 - 5) + (7 - 4)

Remove parentheses

QS = 8 - 5 + 7 - 4

Add and subtract terms

QS = 6

Subchapter links

Lesson Check p.597

Practice and Problem-Solving Exercises p.598-600

Standardized Test Prep p.600

Mixed Review p.600