Question

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

Answer 1

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.