Exercise 21 Page 490

By the Reflexive Property of Equality we know that a number is equal to itself.

Statement	Reason
1. ∠ A exists	1. Given
2. m∠ A=m∠ A	2. Reflexive Property of Equality
3. ∠ A≅ ∠ A	3. Definition of congruent angles

Practice makes perfect

To prove the Reflexive Property of Angle Congruence, we need to prove that a given angle is always congruent to itself. By the Reflexive Property of Equality, we know that the measure of an arbitrary angle is equal to itself. m ∠ A = m ∠ ATwo angles are congruent if they have the same measure. Therefore, we can say that ∠ A is congruent to itself. ∠ A ≅ ∠ A Let's show this as a two-column proof.

Statement	Reason
1. ∠ A exists	1. Given
2. m∠ A=m∠ A	2. Reflexive Property of Equality
3. ∠ A≅ ∠ A	3. Definition of congruent angles

1 Conditional Statements p.488

2 Inductive and Deductive Reasoning p.488

3 Postulates and Diagrams p.489

4 Proving Statements about Segments and Angles p.490

5 Proving Geometric Relationships p.490

Hints