SOLUTION: I really need help. i haven't done math in 13 years. I must do a proof. There are 2 triangles. one on top of the other only the top one is upside down. My given is segment AB is pa

Algebra ->  Geometry-proofs -> SOLUTION: I really need help. i haven't done math in 13 years. I must do a proof. There are 2 triangles. one on top of the other only the top one is upside down. My given is segment AB is pa      Log On


   

Question 251946: I really need help. i haven't done math in 13 years. I must do a proof. There are 2 triangles. one on top of the other only the top one is upside down. My given is segment AB is parallel to segment CD. those being the bases of each triangle. I must prove the top triangle APB is similar to the lower triangle DPC. the 2 triangles are sitting tip to tip not covering each other at all. face to face if u want to call it that thanks for your help
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


AD is a transversal of the two given parallel segments, so angle A is congruent to angle D because of the congruence of opposite interior angles.

BC is a transversal of the two given parallel segments, so angle B is congruent to angle C -- same reason.

Angle APB is congruent to angle CPD because they are vertical angles (formed by the intersection of two straight lines)

The two triangles are similar by Angle-Angle-Angle.


John

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I must do a proof. There are 2 triangles. one on top of the other only the top one is upside down. My given is segment AB is parallel to segment CD. those being the bases of each triangle. I must prove the top triangle APB is similar to the lower triangle DPC. the 2 triangles are sitting tip to tip not covering each other at all. face to face if u want to call it that thanks for your help
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The angles at the tip are vertical angles and are equal to one another.
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The line segment joining the parallel lines are transversals so the
alternate interior angles are equal.
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Three angles of one triangle are equal to three angles in the other.
The triangles are similar by AAA.
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Hope that helps.
Cheers,
Stan H.