Provide reasons for the proof. given: ∠1 ≅∠3 and prove: lt || mv

Proof:

Statement                                                   Reason

1. PV || QM                                                   Given

2. ∠1 is supplementary to ∠2                    Same-Side Interior Angles Theorem

3. m∠1 + m∠2 = 180°                                   Same-Side Interior Angle Theorem

4. ∠1 ≅ ∠3                                                   Given

5. m∠1 = m∠3                                              Definition of Congruent angles  => (If the angles are congruent, the measurements will be equal)

6. m∠3 + m∠2 = 180°                                Same side interior angle theorem (two angles on the same side make 180° if directly next to each other)

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