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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Solutions

Chapter
Section
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem

Complete all missing statements and reasons in the following proof.

Given: Δ R U V R V and 1 3
Prove: Δ S T U is an isosceles triangle

Proof
Statements Reasons
1. Δ R U V ; R V 1. _ _ _ _ _ _ _ _ _
2. U V ¯ U R ¯ 2. _ _ _ _ _ _ _ _ _
3. _ _ _ _ _ _ _ _ _ 3. Given
4. Δ R S U Δ V T U 4. _ _ _ _ _ _ _ _ _
5 . _ _ _ _ _ _ _ _ _ 5 . CPCTC
6 _ _ _ _ _ _ _ _ _ 6 . If 2 sides of a Δ are , this triangle is an isosceles triangle.

To determine

To complete:

The missing statement and reasons, if RV and 13 in triangle ΔRUV.

Explanation

Approach:

The pairs of interior angles are congruent if two parallel lines are cut by a transversal.

Calculation:

Consider the given triangle.

The proof for the given statement is as follows.

Proof
Statements Reasons
1. ΔRUV;RV 1. Given.
2. UV¯UR¯ 2. The two opposite sides of a triangle is congruent if the corresponding angles are congruent.
3.13 3. Given.
4. ΔRSUΔVTU 4. The pairs of angle R and V, angle 1 and 3 are congruent and UV¯UR¯.
So, the condition is AAS.
5. US¯UT¯ 5. CPCTC
6. ΔSTU is an isosceles triangle. 6. If two sides of a Δ are , this triangle is an isosceles triangle

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