Question 547240: Given: GH is parrallel to HJ, KJ is parallel to HJ,
Prove: Triangle GHJ is congruent to Triangle KJH (use AAS theorem)
PLEASE HELP
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! You got something wrong, because what you wrote makes no sense.
If GHJ is a triangle, it cannot have two parallel sides. And since GH and HJ meet at H, they could form an angle, or be part of the same line, but they would not be parallel.
Maybe GHKJ is a parallelogram, with GH parallel to KJ, and HK parallel to GJ.
That would make two triangles sharing side HJ (one congruent side), and having congruent angles because of the lines being parallel.
If GH is perpendicular to HJ, angle GHJ is a right angle.
If KJ is perpendicular to HJ, angle KJH is a right angle.
If you also knew that the angles at G (angle HGJ) and at K (angle JKH) are congruent, The triangles would have AAS congruence. They have two pairs of congruent angles (the pair of right angles, and the pair of G and K). That accounts for the AA (angle, angle) congruency part. Also, one side of each triangle is congruent with a side of the other triangle (side HJ, which is shared between the two triangles, is congruent with itself). That would add an S (side) to the congruent set. And since that side is not between the two angles, we call its AAS, with the S not in between the A's.
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