   Chapter 3.CT, Problem 18CT Elementary Geometry for College St...

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

Solutions

Chapter
Section 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;∠R≅∠V 1. Given. 2. UV¯≅UR¯ 2. The two opposite sides of a triangle is congruent if the corresponding angles are congruent. 3.∠1≅∠3 3. Given. 4. ΔRSU≅ΔVTU 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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