m Which lines are parallel if angle 6 and 7 are congruent? Justify your answer
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4/5 6/
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8 7/
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Lines 3 and 5 are parallel if angle 6 and 7 are congruent.
Justification: If angle 6 and 7 are congruent, then the corresponding angles formed by transversal line 4/5 and line 6/1 are congruent by the vertical angles theorem. Since corresponding angles formed by a transversal crossing two parallel lines are congruent, this means that angle 4 and angle 6 are congruent.
Similarly, the corresponding angles formed by transversal line 8 and line 7/2 are congruent by the vertical angles theorem. Since angle 4 and angle 6 are congruent, this means that angle 8 and angle 7 are congruent.
Therefore, lines 3 and 5 are parallel because angle 8 and angle 7 are congruent and the corresponding angles formed by a transversal crossing two parallel lines are congruent.
Which lines are parallel if angle 5 and 1 are supplementary?
Justify your answer
Lines 2 and 4 are parallel if angle 5 and angle 1 are supplementary.
Justification: If angle 5 and angle 1 are supplementary, then the corresponding angles formed by transversal line 2 and line 5 are congruent by the vertical angles theorem. Since corresponding angles formed by a transversal crossing two parallel lines are congruent, this means that angle 2 and angle 5 are congruent.
Similarly, the corresponding angles formed by transversal line 4 and line 1 are congruent by the vertical angles theorem. Since angle 2 and angle 5 are congruent, this means that angle 4 and angle 1 are congruent.
Therefore, lines 2 and 4 are parallel because angle 4 and angle 1 are congruent and the corresponding angles formed by a transversal crossing two parallel lines are congruent.