Prove that the opposite angles of a parallelogram are congruent.

Question

anonymous · Answer

attachment

anonymous · Answer

they are congruent because when you make it straight the two parallel sides are congruent

anonymous · Answer

I need a proof, Amrut. I don't know how to.

ganeshie8 · Answer

you may try proving the two triangles are congruent and then use CPCTC

anonymous · Answer

Could you walk me through it so I know how to?

ganeshie8 · Answer

sure :)
by definition of parallelogram, opposite sides are congruent + parallel right ?

anonymous · Answer

Yes.

ganeshie8 · Answer

1) $BC \cong AD$ , $AB \cong DC$      ----- By definition of parallelogram

anonymous · Answer

Okay, I see that.

ganeshie8 · Answer

2) $BD \cong BD$ ---- By reflexive property

ganeshie8 · Answer

3) $\triangle ABD \cong \triangle CDB $ ---- By SSS congruence

anonymous · Answer

Now why is that? Number three, I mean.

ganeshie8 · Answer

all 3 sides of triangle ABD are congruent to correspodnign sides of triangle CDB. so the triangles are congruent

ganeshie8 · Answer

its called SSS congruence

anonymous · Answer

Oh, okay. All right. Sweet.

ganeshie8 · Answer

:)
final wud be trivial

4) $\angle A \cong \angle C$ ---- By CPCTC

ganeshie8 · Answer

observe that A and C are opposite angles of given parallelogram. so we have just proved A and C are equal !

anonymous · Answer

Thank you so much! I really appreciate your time and effort. I'm pretty much ignorant on how to reward people on this site. What do I do?

ganeshie8 · Answer

cool :) glad u understood the proof !!

anonymous · Answer

im new too

ganeshie8 · Answer

welcome aboard newbies :) this site is very userfriendly so... you wil get use to the site pretty quickly good luck !!