Question

2.5 angle proofs
1 given: ∠pqr is a right angle
prove: ∠pqs and ∠sqr are complementary
statements reasons

1. ∠pqr is a right angle 1.
2. m∠pqr = 90° 2.
3. m∠pqs + m∠sqr = m∠pqr 3.
4. m∠pqs + m∠sqr = 90° 4.
5. ∠pqs and ∠sqr are complementary 5.

Explanation:

Step1: Given information

Given

Step2: Definition of right - angle

Definition of a right - angle (A right - angle has a measure of 90°)

Step3: Angle - addition postulate

Angle - addition postulate (If point S lies in the interior of ∠PQR, then m∠PQS + m∠SQR=m∠PQR)

Step4: Substitution property

Substitution property (Substitute m∠PQR = 90° into m∠PQS + m∠SQR=m∠PQR)

Step5: Definition of complementary angles

Definition of complementary angles (Two angles are complementary if the sum of their measures is 90°)

Answer:

1. Given
2. Definition of a right - angle
3. Angle - addition postulate
4. Substitution property
5. Definition of complementary angles