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Elementary Geometry for College St...

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

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Given: H J bisects K H L
H J ¯ K L ¯
In Exercise 15, you cam delete Step 5 and 6 and still prove that “ K L ”. What reason would you use to establish that K L in the shorter proof.
Chapter 3.2, Problem 16E, Given: HJ bisects KHL HJKL In Exercise 15, you cam delete Step 5 and 6 and still prove that KL. What
Prove: K L
PROOF
Statements Reasons
1. ? 1. Given
2. J H K J H L 2. ?
3. H J ¯ K L ¯ 3. ?
4. H J K H J L 4. ?
5. ? 5. Identity
6. ? 6. ASA
7. K L 7. ?

To determine

To prove:

The given statement.

Explanation

Given:

The following figure shows the given diagram.

Given that,

HJ bisects KHL and,

HJ¯KL¯

If two angles of a triangle are congruent, then the third angle will also be congruent.

Approach:

The completed proof is shown in the following table.

PROOF
Statements Reasons
1. HJ bisects KHL 1. Given
2. JHKJHL 2. HJ bisects KHL in two equal parts.
3. HJ¯KL¯ 3. Given
4. HJKHJL 4. HJ¯KL¯ and KJ¯JL¯
5

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