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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

8. Geometric Probability

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Exercise 48 Page 674

Write a proportion using the Side-Splitter Theorem or its Corollary.

D

Practice makes perfect

Let's analyze the given figure.

Since we are given a triangle with a line that is parallel to one of its sides, we can use the Side-Splitter Theorem.

By this theorem, we know that the lengths of the segments intersected by the parallel line are proportional. Let's write a proportion using the expressions for the lengths of the segments. 3x/4=x+2/2 Let's solve it for x.

3x/4=x+2/2

▼

Solve for x

LHS * 4=RHS* 4

3x=4*(x+2)/2

a * b/c= a/c* b

3x=4/2*(x+2)

Calculate quotient

3x=2(x+2)

Distribute 2

3x=2x+4

LHS-2x=RHS-2x

x=4

Therefore, the answer is D.

Subchapter links

Lesson Check p.671

Practice and Problem-Solving Exercises p.671-673

Standardized Test Prep p.674

Mixed Review p.674