Question

1. justify the following proof.

given: n || p, ∠9 and ∠6 are supplementary
prove: l || m.
statements reason

1. n || p 1. given
2. ∠9 and ∠6 are supp 2. given
3. ∠9 = ∠7 3. alternate int. ∠s
4. m∠9 = m∠7 4. definition of ≅
5. m∠9 + m∠6 = 180° 5. substitution
6. m∠7 + m∠6 = 180 6. substitution property
7. l || m 7. ____

Explanation:

Step1: State given facts

Given $n\parallel p$ and $\angle9$ and $\angle6$ are supplementary.

Step2: Use alternate - interior angles property

Since $n\parallel p$, $\angle9\cong\angle7$ (alternate interior angles are congruent).

Step3: Define congruent angles

By the definition of congruent angles, $m\angle9 = m\angle7$.

Step4: Substitute equal - angle measures

Given $m\angle9+m\angle6 = 180^{\circ}$, and since $m\angle9 = m\angle7$, we substitute to get $m\angle7+m\angle6 = 180^{\circ}$.

Step5: Apply parallel - line theorem

If two lines are cut by a transversal such that same - side interior angles are supplementary, then the lines are parallel. Since $\angle7$ and $\angle6$ are same - side interior angles and $m\angle7+m\angle6 = 180^{\circ}$, we can conclude that $l\parallel m$. The reason for step 7 is "If same - side interior angles are supplementary, then the lines are parallel".

Answer:

The reason for step 7 is "If same - side interior angles are supplementary, then the lines are parallel".