SOLUTION: you have a parallelogram made up of two triangles (triangle RST and triangle RUT). Given: line segment RU is parallel to line segment ST angle S is congruent to angle U P

Algebra ->  Geometry-proofs -> SOLUTION: you have a parallelogram made up of two triangles (triangle RST and triangle RUT). Given: line segment RU is parallel to line segment ST angle S is congruent to angle U P      Log On


   

Question 290353: you have a parallelogram made up of two triangles (triangle RST and triangle RUT).
Given: line segment RU is parallel to line segment ST
angle S is congruent to angle U
Prove: line segment RS is congruent to line segment TU

how can i do this?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Draw the figure so you can see it.
Mark the angles U and S as equal
mark the line segments RU and ST as congruent
mark the diagonal RT as congruent with RT in the two triangles RUT and RST since they are the same line segment.
Now you have two sides and and angle that are congruent. Therefore the two triangles are congruent and so the third sides RS and UT are congruent

I bet you don't know from the beginning that it is a parallelogram. If you did then the whole proof is unnecessary.since opposite sides in a parallelogram are parallel and congruent.