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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

5. Proportions in Triangles

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Exercise 51 Page 478

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

20

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.

The lengths of the segments intercepted by the parallel line are proportional. Let's write a proportion using the expressions for the lengths of the segments. 30/12=2x+10/x Let's solve it using the Cross Product Property.

30/12=2x+10/x

Cross multiply

30x=12(2x+10)

▼

Solve for x

Distribute 12

30x=24x+120

LHS-24x=RHS-24x

6x=120

.LHS /6.=.RHS /6.

x=20

Subchapter links

Lesson Check p.474

Standardized Test Prep p.478

Mixed Review p.478