Chapter 5.3, Problem 24E

### 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 Exercises 17 to 24, complete each proof.Given: A B ¯ ∥ D C ¯ , A C ¯ ∥ D E ¯ Prove: A B D C = B C C E PROOF Statements Reasons 1. A B ¯ ∥ D C ¯ 2.3. ?4. ∠ A C B ≅ ∠ E 5. Δ A C B ∼ Δ D E C 6. ? 1. ?2. If 2 || lines are cut by a transversal, corresponding ∠ s are ≅ .3. Given4. ?5. ?6. ?

To determine

To prove:

The statement ABDC=BCCE if the sides AB and DC are parallel, AB¯DC¯ and the sides AC and DE are parallel, AC¯DE¯.

Explanation

Definition:

AA:

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

CSSTP:

Corresponding sides of similar triangles are proportional.

Description:

Given that RSÂ¯âˆ¥UVÂ¯.

The given figure is shown below.

Figure

From the given figure, it is observed that the sides AB and DC are parallel, ABÂ¯âˆ¥DCÂ¯.

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

Therefore, âˆ BACâ‰…âˆ D.

From the given figure, it is also observed that the sides AC and DE are parallel, ACÂ¯âˆ¥DEÂ¯.

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

Therefore, âˆ ACBâ‰…âˆ E.

The above mentioned AA definition, the two triangles ACB and DEC are similar since the two angles of one triangle are congruent to two angles of another triangle. Hence, Î”ACBâˆ¼Î”DEC.

From the definition of CSSTP, corresponding sides of similar triangles are proportional

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