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Elementary Geometry for College St...

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

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BuyFindarrow_forward

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

Chapter 5.3, Problem 20E, In Exercises 17 to 24, complete each proof. Given: HJJF,HGFG See figure for Exercise 19. Prove:

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. sG and J are right s 2. ?
3. GJ 3. ?
4. HKJGKF 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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