Question

∠p and ∠q are complementary and ∠r and ∠p are complementary. complete the proof that ∠q≅∠r.
statement\treason
1 ∠p and ∠q are complementary\t
2 ∠r and ∠p are complementary\t
3 m∠p + m∠q = 90°\t
4 m∠r + m∠p = 90°\t
5 m∠p + m∠q = m∠r + m∠p\t
6 m∠q = m∠r\t
7 ∠q≅∠r\t

Explanation:

Step1: Given information

Given

Step2: Given information

Given

Step3: Definition of complementary angles

If two angles are complementary, their sum is 90°.

Step4: Definition of complementary angles

If two angles are complementary, their sum is 90°.

Step5: Transitive property of equality

Since \(m\angle P + m\angle Q=90^{\circ}\) and \(m\angle R + m\angle P = 90^{\circ}\), we can set them equal.

Step6: Subtraction property of equality

Subtract \(m\angle P\) from both sides of \(m\angle P + m\angle Q=m\angle R + m\angle P\).

Step7: Definition of congruent angles

If the measures of two angles are equal, the angles are congruent.

Answer:

1. Given
2. Given
3. Definition of complementary angles
4. Definition of complementary angles
5. Transitive property of equality
6. Subtraction property of equality
7. Definition of congruent angles