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Proofs whole page for 50 points ( serious answers only or report and 1 star )

Proofs whole page for 50 points ( serious answers only or report and 1 star )-example-1
User LeBird
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Question 1:

1) Given - It is given in the problem

2) Corresponding Angles Postulate - If a transversal (line l) intersects two parallel lines (line h and line g), then the corresponding angles must be equal.

3) Transitive Property of Congruence - Since it's given that
\angle1\cong\angle5 and we showed in line 2 that
\angle1\cong\angle2, it should be true that
\angle2\cong\angle5

4) Converse of Corresponding Angles Postulate - If a transversal (line g) intersects two lines (lines l and m), and the corresponding angles that form have equal measure, then the lines are parallel.

Question 2:

1) Given - It is given in the problem

2) Definition of Angle Bisector - It's given that
\overline{DC} bisects
\angle BDE, which means that
\overline{DC} is the angle bisector, and the angle is divided into two angles of the same measure.

3) Transitive Property of Congruence - Since we showed in line 2 that
\angle1\cong\angle2 and its given that
\angle2\cong\angle3, it should be true that
\angle1\cong\angle3

4) Converse of the Alternate Interior Angles Theorem - If a transversal (
\overline{BD}) intersects two lines (
\overline{AB} and
\overline{CD}) and the alternate interior angles formed have the same measure, then the lines are parallel.

User Biswajit Biswas
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8.1k points

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