1.Provide reasons for the statements. Given: and are vertical angles. Prove: StatementReason 1. and are vertical angles. 1. Given 2. and form a linear pair. and form a linear pair. 2. Definition of linear pair 3. and are supplementary. and are supplementary. 3. 4. 4. 5. 5. 6. 6. 7. 7.  

1. ∠1 and ∠3 are vertical angles. 1. Given

2. ∠1 and ∠2 form a linear pair. VAT

∠2 and ∠3 form a linear pair. 2. Definition of linear pair

3. ∠1 and ∠2 are supplementary. Substitution Property

∠2 and ∠3 are supplementary. SAME SIDE INTERIOR ANGLES THEOREM

3. VERTICAL ANGLES THEOREM

4. m∠1 + m∠2 = 180˚ SAME SIDE INTERIOR ANGLES THEOREM

 m∠2 + m∠3 = 180˚ SAME SIDE INTERIOR ANGLES THEOREM

5. m∠1 + m∠2 = m∠2 + m∠3  

(SUBSTITUTION PROPERTY)

6. m∠1 = m∠3 opposite angles

7. ∠1 ≅ ∠3 7. Given

Explanation: