Thread: Triangle Prove

RS bisects PQ at T. PQ bisects RS at T.
Prove: Triangle PTS congruent Triangle QTR

Again, a figure is missing, but it's not so bad as the other post.

Figure not necessarily drawn to scale.

Have you drawn a figure? Always draw one. It helps you visualize how to write your proof. From your given, I labeled the congruent parts of the triangle. It is very obvious to see that the triangles can be proved congruent by using the S.A.S. Postulate. But before that, we need to prove that the corresponding parts are congruent.

Fill in the blanks:
RS bisects PQ at t, then PT ___ TQ (justified by definition of bisectors)
PQ bisects RS at t, then RT ___ TS (again, by definition of bisectors)
<PTR and <QTS are vertical angles. Therefore, they're ___________. (Theorem: all vertical angles are congruent)
Triangle PTS is _______ to triangle QTR. (Justified by the S.A.S postulate)

Originally Posted by Chop Suey

Again, a figure is missing, but it's not so bad as the other post.

Figure not necessarily drawn to scale.

Have you drawn a figure? Always draw one. It helps you visualize how to write your proof. From your given, I labeled the congruent parts of the triangle. It is very obvious to see that the triangles can be proved congruent by using the S.A.S. Postulate. But before that, we need to prove that the corresponding parts are congruent.

Fill in the blanks:
RS bisects PQ at t, then PT ___ TQ (justified by definition of bisectors)
PQ bisects RS at t, then RT ___ TS (again, by definition of bisectors)
<PTR and <QTS are vertical angles. Therefore, they're ___________. (Theorem: all vertical angles are congruent)
Triangle PTS is _______ to triangle QTR. (Justified by the S.A.S postulate)

Thanks for the picture and your effort. I will fill in the blanks later tonight or tomorrow.