Chapter 4.2, Problem 19E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# In Exercises 19 to 24, complete each proof. Given: ∠ 1 ≅ ∠ 2   a n d   ∠ 3 ≅ ∠ 4   Prove: M N P Q is a kite PROOF Statements Reasons 1. ∠ 1 ≅ ∠ 2   a n d   ∠ 3 ≅ ∠ 4 1. ? 2. N Q ¯ ≅ N Q ¯ 2. ? 3. ? 3. ASA 4. M N ¯ ≅ P N ¯ and M Q ¯ ≅ P Q ¯ 4. ? 5. ? 5. If a quadrilateral has two pairs of ≅ adjacent sides, it is a kite

To determine

To complete:

The each proof.

 PROOF Statements Reasons 1. ∠1≅∠2 and ∠3≅∠4 1. ? 2. NQ¯≅NQ¯ 2. ? 3. ? 3. ASA 4. MN¯≅PN¯ and MQ¯≅PQ¯ 4. ? 5. ? 5. If a quadrilateral has two pairs of ≅ adjacent sides, it is a kite
Explanation

Given,

âˆ 1â‰…âˆ 2 and âˆ 3â‰…âˆ 4

Completion of the proof,

 PROOF Statements Reasons 1. âˆ 1â‰…âˆ 2 and âˆ 3â‰…âˆ 4 1. Given 2. NQÂ¯â‰…NQÂ¯ 2. Identity 3. âˆ†MNQâ‰…âˆ†PNQ 3. ASA 4. MNÂ¯â‰…PNÂ¯ and MQÂ¯â‰…PQÂ¯ 4. CPCTC 5. MNPQ is a kite. 5

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