Answer reason 2. ZYXW is a parallelogram W Prove: ZZWX = ZZYX Statements ZY // WX ZW // WZ ZWXZZYZX ZWZX LYXZ ZX ZX AWZX AYXZ ZZWX ZZYX Reasons Given 1 2 Reflexive postulate 3 4

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
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HELP ME PLEASE! i don't understand this well.

**Answer Reason 2**

**ZYWX is a Parallelogram**

Diagram: A parallelogram ZYXW is shown, with diagonals ZX and WY intersecting.

**Prove: ∠ZWX ≅ ∠ZYX**

| **Statements**               | **Reasons**             |
|------------------------------|-------------------------|
| \( \overline{ZY} \parallel \overline{WX} \) <br> \( \overline{ZW} \parallel \overline{YZ} \) | Given                   |
| \( \angle WXZ \cong \angle YZX \)           | 1                       |
| \( \angle WZX \cong \angle YXZ \)           | 2                       |
| \( \overline{ZX} \cong \overline{ZX} \)     | Reflexive Postulate     |
| \( \triangle WZX \cong \triangle YXZ \)     | 3                       |
| \( \angle ZWX \cong \angle ZYX \)           | 4                       |

**Explanation of Diagram:**

The diagram shows a parallelogram ZYXW with a diagonal ZX. The parallel lines ZY & WX and ZW & YZ are indicated, setting up the basis for proving congruent angles through alternate interior angles, and the reflexive property of equality for line ZX establishes triangle congruency.
Transcribed Image Text:**Answer Reason 2** **ZYWX is a Parallelogram** Diagram: A parallelogram ZYXW is shown, with diagonals ZX and WY intersecting. **Prove: ∠ZWX ≅ ∠ZYX** | **Statements** | **Reasons** | |------------------------------|-------------------------| | \( \overline{ZY} \parallel \overline{WX} \) <br> \( \overline{ZW} \parallel \overline{YZ} \) | Given | | \( \angle WXZ \cong \angle YZX \) | 1 | | \( \angle WZX \cong \angle YXZ \) | 2 | | \( \overline{ZX} \cong \overline{ZX} \) | Reflexive Postulate | | \( \triangle WZX \cong \triangle YXZ \) | 3 | | \( \angle ZWX \cong \angle ZYX \) | 4 | **Explanation of Diagram:** The diagram shows a parallelogram ZYXW with a diagonal ZX. The parallel lines ZY & WX and ZW & YZ are indicated, setting up the basis for proving congruent angles through alternate interior angles, and the reflexive property of equality for line ZX establishes triangle congruency.
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