   Chapter 5.3, Problem 36E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

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

Provide a paragraph proof for the following problem.Given: R S ¯ ∥ Y Z ¯ , R U ¯ ∥ X Z ¯ Prove: R S ⋅ Z X = Z Y ⋅ R T To determine

To prove:

The statement RSZX=ZYRT if the sides RS and YZ are parallel, RS¯YZ¯ and the sides RU and XZ are parallel, RU¯XZ¯.

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 RS¯YZ¯,RU¯XZ¯.

The given figure is shown below.

Figure

From the given figure, it is observed that the sides RS and YZ are parallel, RS¯YZ¯.

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

Therefore, RSTY.

From the given figure, it is also observed that the sides RU and XZ are parallel, RU¯XZ¯

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