Chapter 5.3, Problem 33E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# In Exercise 33, provide a two-column proof.Given:                         A B ¯ ∥ D F ¯ , B D ¯ ∥ F G ¯ Prove:                         Δ A B C ∼ Δ E F G

To determine

To prove:

The statement ΔABCΔEFG if the sides AB¯ and DF¯ are parallel, AB¯DF¯ and the sides BD¯ and FG¯ are parallel, BD¯FG¯.

Explanation

Definition:

AA:

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Description:

Given that ABÂ¯âˆ¥DFÂ¯ and BDÂ¯âˆ¥FGÂ¯.

The given figure is shown below.

Figure

From the given figure, it is observed that the sides ABÂ¯ and DFÂ¯ are parallel, ABÂ¯âˆ¥DFÂ¯ and the sides BDÂ¯ and FGÂ¯ are parallel, BDÂ¯âˆ¥FGÂ¯.

Consider ABÂ¯âˆ¥DFÂ¯.

If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

Therefore, âˆ Aâ‰…âˆ FEG

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