Exterior Angle Theorem Proof Practice worksheet with two triangle problems and proof tables.

Here are the completed proofs for the Exterior Angle Theorem practice worksheet.

Problem 1

Goal: Prove that $m\angle3 + m\angle4 = m\angle6$

| Statements | Reasons |
| :--- | :--- |
| 1. A triangle has angles 3, 4, 5 and exterior angle 6 | 1. Given |
| 2. $m\angle3 + m\angle4 + m\angle5 = 180^{\circ}$ | 2. Triangle Angle Sum Theorem |
| 3. $m\angle5 + m\angle6 = 180^{\circ}$ | 3. Linear Pair Postulate (Angles on a straight line add to 180°) |
| 4. $m\angle3 + m\angle4 + m\angle5 = m\angle5 + m\angle6$ | 4. Substitution Property (Both sums equal 180°) |
| 5. $m\angle3 + m\angle4 = m\angle6$ | 5. Subtraction Property of Equality (Subtract $m\angle5$ from both sides) |

***

Problem 2

Goal: Prove that $m\angle5 + m\angle6 = m\angle8$

| Statements | Reasons |
| :--- | :--- |
| 1. A triangle has angles 5, 6, 7 and exterior angle 8 | 1. Given |
| 2. $m\angle5 + m\angle6 + m\angle7 = 180^{\circ}$ | 2. Triangle Angle Sum Theorem |
| 3. $m\angle7 + m\angle8 = 180^{\circ}$ | 3. Linear Pair Postulate |
| 4. $m\angle5 + m\angle6 + m\angle7 = m\angle7 + m\angle8$ | 4. Substitution Property |
| 5. $m\angle5 + m\angle6 = m\angle8$ | 5. Subtraction Property of Equality |