   Chapter 5.3, Problem 20E ### 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
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# In Exercises 17 to 24, complete each proof.Given: H J ¯ ⊥ J F ¯ , H G ¯ ⊥ F G ¯ (See figure for Exercise 19.)Prove: Δ H J K ∼ Δ F G K Exercises 19, 20 PROOF Statements Reasons 1. ? 1. Given 2. ∠ s   G and J are right ∠ s 2. ? 3. ∠ G ≅ ∠ J 3. ? 4. ∠ H K J ≅ ∠ G K F 4. ? 5. ? 5. ?

To determine

To complete:

The proof by using given information.

Explanation

Given:

Given: HJ¯JF¯,HG¯FG¯

Prove: ΔHJKΔFGK

 PROOF Statements Reasons 1. ? 1. Given 2. ∠s G and J are right ∠s 2. ? 3. ∠G≅∠J 3. ? 4. ∠HKJ≅∠GKF 4. ? 5. ? 5. ?

Definition:

AA:

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

Description:

Given that HJ¯JF¯,HG¯FG¯.

To Prove: ΔHJKΔFGK

If two lines are perpendicular, then they form a right angle. Hence, the angles G and J are right angles.

It is known that all right angles are congruent. So that GJ.

If two angles are vertical angles, then they are congruent. That is, HKJFKG

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