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High school geometry

Lesson 6: Proving relationships using similarity

Prove theorems using similarity

In the following triangle,

\frac{E C}{A E} = \frac{D B}{A D}

Below is the proof that

\overset{―}{E D} ∥ \overset{―}{C B}

. The proof is divided into two parts, where the title of each part indicates its main purpose.

Complete part B of the proof.

	Statement	Reason
8	$∠ A ≅ ∠ A$ ‍	Reflexive property
9	$△ A E D \sim △$ ‍	similarity (Part A, 8)
10	$∠ 1 ≅ ∠ 2$ ‍	Measures of corresponding angles of similar triangles are equal. (9)
11	$\overset{―}{E D} ∥ \overset{―}{C B}$ ‍	If a transversal crosses two lines and angles are congruent, then the lines are parallel. (10)

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