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Course: Geometry (FL B.E.S.T.)>Unit 6

Lesson 5: Proving relationships using similarity

Prove theorems using similarity

Problem

In the following triangle, $\frac{EC}{AE}=\frac{DB}{AD}$.
Below is the proof that $\stackrel{―}{ED}\parallel \stackrel{―}{CB}$. The proof is divided into two parts, where the title of each part indicates its main purpose.
Complete part B of the proof.

Part B: Prove $\stackrel{―}{ED}\parallel \stackrel{―}{CB}$‍

StatementReason
8$\mathrm{\angle }A\cong \mathrm{\angle }A$Reflexive property
9$\mathrm{△}AED\sim \mathrm{△}$
similarity (Part A, 8)
10$\mathrm{\angle }1\cong \mathrm{\angle }2$Measures of corresponding angles of similar triangles are equal. (9)
11$\stackrel{―}{ED}\parallel \stackrel{―}{CB}$If a transversal crosses two lines and
angles are congruent, then the lines are parallel. (10)