6. given: ( l parallel m ; angle 4 cong angle 7 ) prove: ( angle 8 ) and ( angle 9 ) are supplementary

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Accepted Answer

# Explanation:
## Step1: Use the property of parallel lines
Since $l\parallel m$, by the alternate - interior angles theorem, $\angle7=\angle2$. Given $\angle4 = \angle7$, then $\angle4=\angle2$ (transitive property of congruence).
## Step2: Use the property of parallel lines again
If $\angle4=\angle2$, then $AD\parallel BE$ (if alternate - interior angles are congruent, then the lines are parallel).
## Step3: Use the property of parallel lines for the new pair of parallel lines
Since $AD\parallel BE$, then $\angle8+\angle9 = 180^{\circ}$ (consecutive - interior angles of parallel lines are supplementary).

# Answer:
| Statements | Reasons |
|--|--|
| $l\parallel m$ | Given |
| $\angle7=\angle2$ | Alternate - interior angles theorem |
| $\angle4=\angle7$ | Given |
| $\angle4=\angle2$ | Transitive property of congruence |
| $AD\parallel BE$ | If alternate - interior angles are congruent, then the lines are parallel |
| $\angle8+\angle9 = 180^{\circ}$ | Consecutive - interior angles of parallel lines are supplementary |

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of parallel lines

Step2: Use the property of parallel lines again

Step3: Use the property of parallel lines for the new pair of parallel lines

Answer:

Statements	Reasons
\(\angle7=\angle2\)	Alternate - interior angles theorem
\(\angle4=\angle7\)	Given
\(\angle4=\angle2\)	Transitive property of congruence
\(AD\parallel BE\)	If alternate - interior angles are congruent, then the lines are parallel
\(\angle8+\angle9 = 180^{\circ}\)	Consecutive - interior angles of parallel lines are supplementary