13 Given: m4CXE = mZFZH mZ1 = mZ3 Prove: m2 = mZ4 Statement Reason 1 M2CXE = mZ1+ m2 Reason ? 2 MZFZH = m43 + m24 Reason ? 3 MZCXE = mZ FZH Given 4 m21+ m42 = m43 + m44 Reason ? 5 mZ1= m43 Given 6 m43 + m22 = mZ3 + mZ4 Reason ? 7 m 2 = m24 Reason ?

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Geometric Proof Exercise

#### Diagram Description
The image contains two diagrams of lines and angles. The first diagram includes three sets of intersecting lines labeled with four angles: ∠G, ∠F, ∠E, and ∠D. The second diagram highlights two additional angles: ∠X and ∠C.

#### Problem Statement
**Given:**  
- \( m \angle CXE = m \angle FZH \)  
- \( m \angle 1 = m \angle 3 \)  

**Prove:**  
- \( m \angle 2 = m \angle 4 \)  

#### Proof Table

| Statement                                   | Reason      |
|---------------------------------------------|-------------|
| 1. \( m \angle CXE = m \angle 1 + m \angle 2 \) | Reason ?    |
| 2. \( m \angle FZH = m \angle 3 + m \angle 4 \) | Reason ?    |
| 3. \( m \angle CXE = m \angle FZH \)          | Given       |
| 4. \( m \angle 1 + m \angle 2 = m \angle 3 + m \angle 4 \) | Reason ?  |
| 5. \( m \angle 1 = m \angle 3 \)              | Given       |
| 6. \( m \angle 3 + m \angle 2 = m \angle 3 + m \angle 4 \) | Reason ?  |
| 7. \( m \angle 2 = m \angle 4 \)              | Reason ?    |

#### Explanation
The table demonstrates the structure of the proof, which requires filling in the reasons for each logical step. You'll need to correctly apply geometric theorems or postulates to complete the proof.
Transcribed Image Text:### Geometric Proof Exercise #### Diagram Description The image contains two diagrams of lines and angles. The first diagram includes three sets of intersecting lines labeled with four angles: ∠G, ∠F, ∠E, and ∠D. The second diagram highlights two additional angles: ∠X and ∠C. #### Problem Statement **Given:** - \( m \angle CXE = m \angle FZH \) - \( m \angle 1 = m \angle 3 \) **Prove:** - \( m \angle 2 = m \angle 4 \) #### Proof Table | Statement | Reason | |---------------------------------------------|-------------| | 1. \( m \angle CXE = m \angle 1 + m \angle 2 \) | Reason ? | | 2. \( m \angle FZH = m \angle 3 + m \angle 4 \) | Reason ? | | 3. \( m \angle CXE = m \angle FZH \) | Given | | 4. \( m \angle 1 + m \angle 2 = m \angle 3 + m \angle 4 \) | Reason ? | | 5. \( m \angle 1 = m \angle 3 \) | Given | | 6. \( m \angle 3 + m \angle 2 = m \angle 3 + m \angle 4 \) | Reason ? | | 7. \( m \angle 2 = m \angle 4 \) | Reason ? | #### Explanation The table demonstrates the structure of the proof, which requires filling in the reasons for each logical step. You'll need to correctly apply geometric theorems or postulates to complete the proof.
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