SOLUTION: Given: segment TX is parallel to segment SY, angle TXY is congruent to angle TSY Prove: Triangle TSY is congruent to Triangle YXT the diagram looks like this: http://www.mathpla

Algebra ->  Geometry-proofs -> SOLUTION: Given: segment TX is parallel to segment SY, angle TXY is congruent to angle TSY Prove: Triangle TSY is congruent to Triangle YXT the diagram looks like this: http://www.mathpla      Log On


   

Question 683322: Given: segment TX is parallel to segment SY, angle TXY is congruent to angle TSY
Prove: Triangle TSY is congruent to Triangle YXT
the diagram looks like this:
http://www.mathplanet.com/media/44005/parallelogram1_499x300.jpg
But the letters from left to right are:
Top: T then X.
Bottom: S then Y.
Found 2 solutions by solver91311, Onmyoji.S:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

TY = TY by reflexive equality, angle XTY congruent angle TYS by opposite interior angles, two pairs of congruent angles in a triangle means there are three pairs of congruent angles, so angle TYX congruent to angle STY. Now you have triangle congruence by SAS.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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Answer by Onmyoji.S(32) About Me  (Show Source):
You can put this solution on YOUR website!
Given: segment TX is parallel to segment SY, angle TXY is congruent to angle TSY
Prove: Triangle TSY is congruent to Triangle YXT
_________❤________________❤_________________❤_____________
1)segment TX is parallel to segment SY
2)angle XTY congruent angle SYT
3)angle TXY is congruent to angle TSY
4)segment TY congruent segment YT
5)Triangle TSY is congruent to Triangle YXT
_________❤________________❤_________________❤______________
1】Given
2】Alternate interior angle theorem
3】Given
4】Reflexive of properties of congruence
5】AAS
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