SOLUTION: I am trying to understand proofs in geometry the question is ; Given S is the midpoint of line RU and line QT Prove line QR // line TU How do I do this?

Question 1125285: I am trying to understand proofs in geometry the question is ;
Given S is the midpoint of line RU and line QT Prove line QR // line TU
How do I do this?

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

QS = ST and RS = SU, both by defn of midpoint, hence segments QS and ST are congruent and RS and SU are congruent. Angle QSR congruent Angle UST because they are vertical angles. Hence, triangle QSR is congruent to triangle UST. Then angle TUS is congruent to angle QRS by CPCT. Then segment QR parallel to segment TU by equal opposite interior angles of a transversal. You can't actually prove anything about line QR or line TU because QR and TU are line segments, NOT lines. You can claim that the line CONTAINING segment QR is parallel to the line CONTAINING the segment TU.

John

My calculator said it, I believe it, that settles it

RELATED QUESTIONS
I am a 10th grade in geometry. Please help me with this proof. Given: rhombus ABCD,... (answered by Mathtut)

Given: N is the midpoint of line MP, Q is the midpoint of line RP, and line PQ is... (answered by tommyt3rd)

I am so confused on proofs. This is the information given minus the picture. Triagle... (answered by richard1234)

P, Q, R, S and T are on line k such that Q is the midpoint of PT, R is the midpoint of... (answered by jim_thompson5910)

This is a two column proof. I have no idea how to solve proofs. Please help! Given:... (answered by richard1234)

If you are given ΔQSU is isosceles with base line ___. QU ___ ___ RQ... (answered by ramkikk66)

I am very confused about proofs (two column, to be exact). I am in 9th grade Geometry.... (answered by Fombitz,amalm06)

Given: Q is the midpoint of line segment PR and R is the midpoint of line segment QS... (answered by solver91311)

A conjecture and the two-column proof used to prove the conjecture are shown. Given: S (answered by richwmiller)