SOLUTION: Hi, my name is Diane, and I needed a bit of help with this proof. The Given: Kite ABCD & Line AB is congruent to AD and line CB is congruent to CD Prove: Line AC is perpendi

Question 703159: Hi, my name is Diane, and I needed a bit of help with this proof.
The Given: Kite ABCD & Line AB is congruent to AD and line CB is congruent to CD
Prove: Line AC is perpendicular to line BD
To start, I wrote down the given as step 1, and that's where all I know ends. >.< I think I may have an idea of how this goes, but I'm not sure. I was thinking that I could first prove the center point (point E) congruent to itself, then I could somehow prove the top 2 triangles to be the same. I can't seem to clearly write each step, except I do know, that I would have to prove the that line AC is a angle bisector first, but I can't remember the therorem that proved that. I was wondering if you could help ASAP?
Thank you so so so so so so so very much~!! If you could help that would be absolutely amazing :)
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Looking at triangles ABC and ADC:
AC is congruent with itself.
So triangle ABC is congruent with ADC (Side-Side-Side congruency)
By CPCTC (Corresponding Parts of Congruent Triangles are Congruent),
angles BAC and DAC are congruent, making AC the bisector of angle BAD.

Looking at triangles ABE and ADE:
AE is congruent with itself.
AB is congruent to AD (given)
Angles BAE(=BAC) and DAE(=DAC) are congruent (proven above)
So triangle ABE is congruent with ADE (Side-Angle-Side congruency).
By CPCTC, angles BEA and DEA are congruent,
which makes them right angles, because they add to straight angle BED.

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