Question

PROOF Complete the flow proof of Corollary 5.1. Drag the reasons to complete the proof.

Given: ∠R is a right angle.
Prove: ∠S and ∠T are complementary.

Proof:

Answer 1

The proof can be completed as follows:

1. ZR is a right angle. (Given)
2. m∠R = 90°. (Definition of a right angle)
3. 90° + m∠S + m∠T = 180°. (Triangle Angle-Sum Theorem)
4. m∠S + m∠T = 90°. (Subtraction Property)
5. ZS and T are complementary. (Definition of complementary angles)

The given proof is to show that angle S and angle T are complementary, given that angle R is a right angle. The proof can be completed as follows:

Given: ZR is a right angle.

Prove: ZS and T are complementary.

Proof:

Definition of a right angle: A right angle is defined as an angle measuring 90 degrees.

Given: Since ZR is a right angle, we know m∠R = 90°.

Triangle Angle-Sum Theorem: The sum of the angles in any triangle is 180 degrees.

Substitution: Substitute the known value of m∠R into the Triangle Angle-Sum Theorem: 90° + m∠S + m∠T = 180°

Subtraction Property: Subtract 90° from both sides to isolate m∠S + m∠T: m∠S + m∠T = 90°

Definition of complementary angles: Two angles are complementary if their sum is 90 degrees.

Conclusion: Since we have shown that m∠S + m∠T = 90°, we can conclude that ZS and T are complementary angles.

Therefore, the proof establishes that ZS and T are complementary angles based on the given information that ZR is a right angle.