Question

2 given: ∠2≅∠3;∠1 and ∠2 form a linear pair prove: ∠1 and ∠3 are supplementary statements reasons 1. ∠2≅∠3 1. given 2. m∠2 = m∠3 2. def of congruence 3. ∠1 and ∠2 form a linear pair 3. given 4. ∠1 and ∠2 are supplementary 4. 5. m∠1 + m∠2 = 180° 5. 6. m∠1 + m∠3 = 180° 6. 7. ∠1 and ∠3 are supplementary 7. 3 given: ∠1 and ∠2 form a right - angle; m∠1 + m∠3 = 90° prove: ∠2≅∠3 statements reasons 1. ∠1 and ∠2 form a right angle 1. 2. ∠1 and ∠2 are complementary 2. 3. m∠1 + m∠3 = 90° 3. 4. ∠1 and ∠3 are complementary 4. 5. ∠2≅∠3 5. ©gina wilson (all things algebra, llc) 2014 - 2020

Explanation:

Step1: Recall linear - pair property

If two angles form a linear pair, they are supplementary. So for the first proof:

1. Reason: If two angles form a linear pair, they are supplementary.
2. Reason: Definition of supplementary angles (the sum of the measures of supplementary angles is 180°).
3. Reason: Substitution property (since \(m\angle2 = m\angle3\) from step 2).
4. Reason: Definition of supplementary angles (if \(m\angle1 + m\angle3=180^{\circ}\), then \(\angle1\) and \(\angle3\) are supplementary).

For the second proof:

1. Reason: Given.
2. Reason: If two angles form a right - angle, they are complementary.
3. Reason: Given.
4. Reason: Definition of complementary angles (if \(m\angle1 + m\angle3 = 90^{\circ}\), then \(\angle1\) and \(\angle3\) are complementary).
5. Reason: If two angles are complementary to the same angle, then they are congruent.

Answer:

For problem 2:

1. If two angles form a linear pair, they are supplementary.
2. Definition of supplementary angles.
3. Substitution property.
4. Definition of supplementary angles.

For problem 3:

1. Given.
2. If two angles form a right - angle, they are complementary.
3. Given.
4. Definition of complementary angles.
5. If two angles are complementary to the same angle, then they are congruent.