Question

prove: ∠2≅∠3
statements reasons

1. ∠1 and ∠3 are supplementary 1.
2. m∠1 + m∠3 = 180° 2.
3. 3. definition of linear pair
4. 4.
5. m∠1 + m∠2 = 180° 5.
6. m∠1 + m∠2 = m∠1 + m∠3 6.
7. 7. subtraction property of equality
8. ∠2≅∠3 8.
9. go back to the reflection section of today’s notes on p. 25 and write 2 observations that you saw and 1 question you still have

Explanation:

Step1: Given

1. $\angle1$ and $\angle3$ are supplementary

Step2: Definition of supplementary angles

1. $m\angle1 + m\angle3=180^{\circ}$

Step3: $\angle1$ and $\angle2$ form a linear - pair

1. $\angle1$ and $\angle2$ form a linear pair

Step4: Linear - pair postulate

1. If two angles form a linear pair, then they are supplementary

Step5: Supplementary angles sum to 180 degrees

1. $m\angle1 + m\angle2 = 180^{\circ}$

Step6: Transitive property of equality

1. $m\angle1 + m\angle2=m\angle1 + m\angle3$

Step7: Subtract $m\angle1$ from both sides

1. $m\angle2=m\angle3$

Step8: Definition of congruent angles

1. $\angle2\cong\angle3$

Answer:

1. Given
2. Definition of supplementary angles
3. $\angle1$ and $\angle2$ form a linear pair
4. Linear - pair postulate
5. Definition of supplementary angles
6. Transitive property of equality
7. $m\angle2=m\angle3$
8. Definition of congruent angles