Question

Use a paragraph proof to prove the corresponding angles postulate:

Given: segment A B is parallel to segment C D.

Prove: Corresponding angles are congruent

Transversal EF cuts through parallel lines segments AB and CD creating four sets of corresponding angles; angles 1, 2, 3, 4 are formed by EF and AB; angles 5, 6, 7, 8 are formed by the EF and CD.

Answer 1

@jim_thompson5910

Answer 2

@terenzreignz

Answer 3

angles 1 and 5 are corresponding angles

Answer 4

angles 1 and 3 are vertical angles so they are congruent

angles 3 and 5 are alternate interior angles so they are congruent (because AB || CD)

so by the transitive property angle 1 is congruent to angle 5

this proves that the corresponding angles 1 and 5 are congruent

follow the same steps to prove the other pairs of corresponding angles are congruent

Answer 5

Wait, so that's all included in my paragraph proof?

Answer 6

yes pretty much

and you'll use similar reasoning to prove the other pairs of corresponding angles are congruent

Answer 7

so you'll have to add more

Answer 8

Lines r and s are parallel as given. There are four pairs of corresponding angles: angle 1 and angle 5, angle 2 and angle 6, angle 3 and angle 7, and angle 4 and angle 8. Since r and s are parallel, the slope of r is equal to the slope of s. Since t is a straight line, the slope of t is the same at both intersections, by the definition of a straight line. Thus, the corresponding angles created at both intersections must have the same measure, since the difference of the slopes at each intersection is the same, and the intersections share a common line. So, corresponding angles must have equal measure. Therefore, by definition of congruent angles, corresponding angles are congruent: angle 1 is congruent to angle 5, angle 2 is congruent to angle 6, angle 3 is congruent to angle 7, and angle 4 is congruent to angle 8.