parallelogram - proof

[TheMathNoob]

hello, ABCD is a parallelogram.

beta is bigger than alpha.

I need to proof that AB is bigger than AD, does anyone know how to proof that?

thanks.

 

[Deleted member 4993]

hello, ABCD is a parallelogram.
View attachment 1471
alpha is bigger than beta.

I need to proof that AB is bigger than AD, does anyone know how to proof that?

thanks.

Do you know law of sines? - you can prove through that.

There is a theorem (exact statement of which I forget) - that states that in a triangle the side opposite to larger angle is bigger. That can be used here (along with congruence of triangles ABD and DBC and transverse angle theorems of parallel lines.)

 

[TheMathNoob]

Thank you, I don't know sines, and about the theorem, we didn't learn this theorem in school, where can I learn this theorem?
or maybe I can without this theorem?

 

[Deleted member 4993]

A google search produced following results:

PROPOSITION 18. THEOREM

A greater side of a triangle is opposite a greater angle.

PROPOSITION 19. THEOREM A greater angle of a triangle is opposite a greater side.

 

[TheMathNoob]

Thank you very much.