Example 1a Given: L1 L2,L2 &L4 form fin. pair/1 &L3 form lin. pair. Prove: L3 L4 Statements 1.41€ 22, 224x4 form lin pair; cl +43 2. form lin pair 3. 4. 5. 6. 7<3=24 Reasons 1. Given 2. Defn. L 3. Defn. linear pair 4. Substitution 5. Substitution 6. Subtraction 7. Defn. Ls
Example 1a Given: L1 L2,L2 &L4 form fin. pair/1 &L3 form lin. pair. Prove: L3 L4 Statements 1.41€ 22, 224x4 form lin pair; cl +43 2. form lin pair 3. 4. 5. 6. 7<3=24 Reasons 1. Given 2. Defn. L 3. Defn. linear pair 4. Substitution 5. Substitution 6. Subtraction 7. Defn. Ls
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
Related questions
Question
Prove.
![**Example 1a**
**Given:**
∠1 ≅ ∠2, ∠2 & ∠4 form a linear pair; ∠1 & ∠3 form a linear pair.
**Prove:**
∠3 ≅ ∠4
**Diagram:**
The diagram shows two intersecting lines. Angles 1 and 2 are on one side of a line, with angles 3 and 4 on the opposite side, depicting the given relationships.
**Statements and Reasons:**
1. ∠1 ≅ ∠2; ∠2 & ∠4 form a linear pair; ∠1 & ∠3 form a linear pair
**Reason:** Given
2. ∠2 and ∠4 form a linear pair
**Reason:** Definition of a linear pair
3. ∠1 and ∠3 form a linear pair
**Reason:** Definition of a linear pair
4. [No statement is visible here]
**Reason:** Substitution
5. [No statement is visible here]
**Reason:** Substitution
6. [No statement is visible here]
**Reason:** Subtraction
7. ∠3 ≅ ∠4
**Reason:** Definition of congruent angles
**Note:** Steps 4, 5, and 6 have missing statements, but the reasoning involves substitution and subtraction, leading to the conclusion in step 7.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12a1ba4a-9eea-484c-989f-6e04f409a1c7%2Fdd34dfc9-bfd8-44fe-a07a-71b5534ddf6d%2Fneybv30j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Example 1a**
**Given:**
∠1 ≅ ∠2, ∠2 & ∠4 form a linear pair; ∠1 & ∠3 form a linear pair.
**Prove:**
∠3 ≅ ∠4
**Diagram:**
The diagram shows two intersecting lines. Angles 1 and 2 are on one side of a line, with angles 3 and 4 on the opposite side, depicting the given relationships.
**Statements and Reasons:**
1. ∠1 ≅ ∠2; ∠2 & ∠4 form a linear pair; ∠1 & ∠3 form a linear pair
**Reason:** Given
2. ∠2 and ∠4 form a linear pair
**Reason:** Definition of a linear pair
3. ∠1 and ∠3 form a linear pair
**Reason:** Definition of a linear pair
4. [No statement is visible here]
**Reason:** Substitution
5. [No statement is visible here]
**Reason:** Substitution
6. [No statement is visible here]
**Reason:** Subtraction
7. ∠3 ≅ ∠4
**Reason:** Definition of congruent angles
**Note:** Steps 4, 5, and 6 have missing statements, but the reasoning involves substitution and subtraction, leading to the conclusion in step 7.
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