SOLUTION: Write a proof for each of the following. 1. Given: 𝑚∠1 = 90°;∠1 ≅ ∠2 Prove: ∠2 is a right angle 2. Given: 3(x + 1) = 6(x

SOLUTION: Write a proof for each of the following. 1. Given: 𝑚∠1 = 90°;∠1 ≅ ∠2 Prove: ∠2 is a right angle 2. Given: 3(x + 1) = 6(x - 3) Prove: x = 7 3. Given: 𝑚∠1

Question 1179598: Write a proof for each of the following.
1. Given: 𝑚∠1 = 90°;∠1 ≅ ∠2
Prove: ∠2 is a right angle
2. Given: 3(x + 1) = 6(x - 3)
Prove: x = 7
3. Given: 𝑚∠1 = 180°;∠1 ≅ ∠2; 𝑚∠2 ≅ 𝑚∠3
Prove: ∠3 is a straight angle.
4. Given 8.5s - 81.7 = -9.23s + 148.79
Prove: s = 13
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
You got it! Let's write out the proofs in a clear, structured way.
**1. Given: 𝑚∠1 = 90°; ∠1 ≅ ∠2
Prove: ∠2 is a right angle**
**Proof:**
| Statement | Reason |
|---|---|
| 1. 𝑚∠1 = 90° | Given |
| 2. ∠1 ≅ ∠2 | Given |
| 3. 𝑚∠1 = 𝑚∠2 | Definition of congruent angles (If angles are congruent, their measures are equal) |
| 4. 𝑚∠2 = 90° | Substitution Property of Equality (Substitute 90° for 𝑚∠1 in step 3) |
| 5. ∠2 is a right angle | Definition of a right angle (An angle with a measure of 90° is a right angle) |
**2. Given: 3(x + 1) = 6(x - 3)
Prove: x = 7**
**Proof:**
| Statement | Reason |
|---|---|
| 1. 3(x + 1) = 6(x - 3) | Given |
| 2. 3x + 3 = 6x - 18 | Distributive Property (Multiply through the parentheses) |
| 3. 3x + 21 = 6x | Addition Property of Equality (Add 18 to both sides) |
| 4. 21 = 3x | Subtraction Property of Equality (Subtract 3x from both sides) |
| 5. 7 = x | Division Property of Equality (Divide both sides by 3) |
| 6. x = 7 | Symmetric Property of Equality (If a = b, then b = a) |
**3. Given: 𝑚∠1 = 180°; ∠1 ≅ ∠2; 𝑚∠2 ≅ 𝑚∠3
Prove: ∠3 is a straight angle**
**Proof:**
| Statement | Reason |
|---|---|
| 1. 𝑚∠1 = 180° | Given |
| 2. ∠1 ≅ ∠2 | Given |
| 3. 𝑚∠1 = 𝑚∠2 | Definition of congruent angles |
| 4. 𝑚∠2 = 180° | Substitution Property of Equality (Substitute 180° for 𝑚∠1 in step 3) |
| 5. 𝑚∠2 ≅ 𝑚∠3 | Given |
| 6. 𝑚∠2 = 𝑚∠3 | Definition of congruent angles |
| 7. 𝑚∠3 = 180° | Substitution Property of Equality (Substitute 180° for 𝑚∠2 in step 6) |
| 8. ∠3 is a straight angle | Definition of a straight angle (An angle with a measure of 180° is a straight angle) |
**4. Given: 8.5s - 81.7 = -9.23s + 148.79
Prove: s = 13**
**Proof:**
| Statement | Reason |
|---|---|
| 1. 8.5s - 81.7 = -9.23s + 148.79 | Given |
| 2. 17.73s - 81.7 = 148.79 | Addition Property of Equality (Add 9.23s to both sides) |
| 3. 17.73s = 230.49 | Addition Property of Equality (Add 81.7 to both sides) |
| 4. s = 13 | Division Property of Equality (Divide both sides by 17.73) |

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