1. Given: ∠ABC is a right angle, so ∠1 is complementary to ∠2.
Proof:
1) ∠ABC is a right angle. → Given
2) m∠ABC = 90° → Definition of Right Angle
3) m∠1 + m∠2 = m∠ABC → Angle Addition Postulate
4) m∠1 + m∠2 = 90° → Substitution Property of Equality
5) ∠1 is complementary to ∠2 → Definition of Complementary Angles
2. Given: ∠1 and ∠2 are complementary, and ∠P is complementary to ∠2. Prove: ∠1 ≅ ∠P.
Proof:
1) ∠1 and ∠2 are complementary. → Given
2) m∠1 + m∠2 = 90° → Definition of Complementary Angles
3) ∠P is complementary to ∠2. → Given
4) m∠P + m∠2 = 90° → Definition of Complementary Angles
5) m∠1 + m∠2 = m∠P + m∠2 → Substitution Property of Equality
6) m∠1 = m∠P → Subtraction Property of Equality
7) ∠1 ≅ ∠P → Definition of Congruent Angles
3. Given: RS = 72. Prove: RS = 72.
Proof:
1) RS = 72. → Given
2) RS is the segment. → Definition of segment - Notation
3) RS = 72. → Substitution - Simplify
4) RS = 72. → Definition of Congruent Segments
Parent Tip: Review the logic above to help your child master the concept of geometric proof worksheet.
