Question

Write an indirect proof to show that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

Answer 1

@johnweldon1993 can u please help me !!!

Answer 2

@mathmate please please help me

Answer 3

Do you have the original question?

Answer 4

no all it telling is to Write an indirect proof to show that opposite sides of a parallelogram are congruent

Answer 5

Ok. To start, congruent opposite sides of a parallelogram is one of the properties of a parallelogram. Since we need to prove it, we have to start with the definition of a parallelogram to know what we already know.

According to Wiki:
"In Euclidean geometry, a parallelogram is a (non self-intersecting) quadrilateral with two pairs of parallel sides. "

Are you familiar with congruent triangles, and transversals of parallel lines?

Answer 6

yes I am (:

Answer 7

Good, so this is what we're given with.

We need to prove that AD // BC

Answer 8

* we need to prove that mAD = mBC

Answer 9

@Moo_Moo17
What do you think the approach would be?

Answer 10

im not sure I feel like I know it but I cant remember sorry im trying

Answer 11

The trick is to draw the diagonal BD, then you could prove that triangles ABD and CDB are congruent.
Since AD and BC are corresponding sides, they would be congruent.
I'll let you attempt that, since you are familiar with the tools needed (parallel lines, transversals, congruent triangles).