   Chapter 3.2, Problem 14E ### 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 Exercise 13and 14, complete each proof. Given: H J ¯ ⊥ K L ¯ and H K ¯ ≅ H L ¯ (See figure below)In Exercise 13, you add a Step 6 to prove that “J is the midpoint of K L ¯ .” What reason would you use to establish this conclusion? Prove: J is the midpoint of K L ¯ PROOF Statements Reasons 1. H J ¯ ⊥ K L ¯ and H K ¯ ≅ H L ¯ 1. ? 2. ∠ s H J K and H J L are right ∠ s 2. ? 3. H J ¯ ≅ H J ¯ 3. ? 4. ? 4. HL 5. ? 5. CPCTC 6. J is the midpoint of K L ¯ . 6. ?

To determine

To prove:

The given statement.

Explanation

Given:

The following figure shows the given diagram.

Given that,

HJ¯KL¯ and HK¯HL¯.

Approach:

By definition of hypotenuse leg congruency (HL), if two triangles have corresponding sides that are then triangle will be congruent.

In the step (5) it is proved that KJ¯JL¯, then J will be definitely the midpoint of KL¯.

The completed proof is shown in the following table.

 PROOF Statements Reasons 1. HJ¯⊥KL¯ and HK¯≅HL¯ 1. Given 2. ∠s HJK and HJL are right ∠s 2. HJ¯⊥KL¯ 3. HJ¯≅HJ¯ 3. Identity 4. ΔHJK≅ΔHJL 4. HL 5. KJ¯≅JL¯ 5

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