Question

Prove that the opposite angles of a parallelogram are congruent.

Answer 1

Is it multiple choice or what?

Answer 2

use properties of angles of parallel lines cut by a transversal

im betting that would be the quickest way to prove it

Answer 3

Well the definition of a parallelogram states that you have 2 pairs of parallel sides, hence <A + <B = <B + <C = 180.
Because of that property, we have <A + <B = <B + <C, and a simple cancellation of <B will tell us that <A = <C

Answer 4

@FutureMathProfessor ooo so you would use the definition of a parallelogram to prove it and that is it?

Answer 5

It's all you have to use. No need in overcomplicating things.

Answer 6

@FutureMathProfessor o k so my answer would be similar to the thing you wrote?

Answer 7

AB|| DC and BD cuts it.
\[<2=<4 ....(Alternating angles.)\]
<6=<5 ....(Alternating angles)
<2+<6=<4+<5
<ADC=<ABC
Similarly we can prove <BCD=<<BAD