Select the correct answer. given: transversal t passes through parallel lines r and s. prove: statement reason 1. r || s given 2. for parallel lines cut by a transversal, corresponding angles are congruent. 3. what is the next step in the proof? choose the most logical approach. statement: and reason: congruent supplements theorem statement: and reason: linear pair theorem statement: and reason: definition of supplementary angles statement: and reason: vertical angles theorem

reason: congruent supplements theorem

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.