Question

Prove that opposite sides of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures

Answer 1

@caraonline

Answer 2

You need to split your parallelogram into two triangles:

Answer 3

We can show that opposite sides are congruent by showing that ADB and BDC are congruent

Answer 4

Its because alternate interior angles right?

Answer 5

The line BD is shared. Angle DAB = angle BCD because opposite angles in a parallelogram are equal.

Answer 6

We can also take the alternate angles rule (Z angles) to show that angle ABD = angle BDC

Answer 7

So we have ASA, which shows that the two triangles are congruent. Because ABD = BDC and not ADB, triangle ABD is a reflection of triangle BCD, so opposite sides are equal.

Answer 8

http://library.thinkquest.org/20991/media/geo_pex1.gif so in this 2=4 right? is there a postulate or theorem that proves this?

Answer 9

Exactly, aye. You can just just the alternate angles theorem, I imagine :)

Answer 10

Okay thanks sooo muchhhh!