Chapter 3.2, Problem 5E

### Elementary Geometry for College St...

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

Chapter
Section

### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Exercise 5 to 12, plan and write the two-column proof for each problem. Given: âˆ  1 and âˆ  2 are right âˆ  s C A Â¯ â‰… D A Â¯ Prove: Î” A B C â‰… Î” A B D

To determine

To prove:

The given statement.

Explanation

Given:

The following figure shows the given diagram.

Given that,

âˆ 1 and âˆ 2 are right âˆ s and CAÂ¯â‰…DAÂ¯.

Two right triangles will be congruent if the hypotenuse and corresponding lag are equal in both triangles.

Approach:

The completed proof is shown in the following table.

 Proof Statements Reasons 1. âˆ 1 and âˆ 2 are right âˆ s 1. Given 2. CAÂ¯â‰…DAÂ¯ 2. Given 3. âˆ 1=90Â° 3. Definition of right angle. 4. âˆ 2=90Â° 4. Definition of right angle. 5. âˆ 1â‰…âˆ 2 5. Definition of congruent triangles. 6. ABÂ¯â‰…ABÂ¯ 6

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