Question

Check my answer please? Geometry proofs.

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

Answer 1

This was my answer: A parallelogram typically has two sets of parallel lines.

So, say we had a typical parallelogram (like this one that I drew for this question: http://prntscr.com/91djb0).
Say we wanted to prove that side AB was congruent to side DC and that side AD was congruent to side BC.

If we drew a line intersecting the figure, or a transversal in this case, it would look like this: http://prntscr.com/91dlmc

That transversal will cut the parallelogram into two equal triangles. We will have triangle ABD, with angel ABD. We will also have triangle BDC, with angle BDC.

As shown here, http://prntscr.com/91domn, angles ABD and BDC are alternate interior angles. By the alternate interior angles theorem, if a transversal intersects two parallel lines, then alternate interior angles are congruent.
Therefore, angles ABD and BDC are congruent.

Using these congruent alternate interior angles, we can use the Angle-Side-Angle Postulate to say that triangle ADB is congruent to triangle CBD.

We can also say that side DC and side BA are congruent because they are corresponding sides of congruent triangles.
Similarly, side AD will correspond to side CB.

Therefore, we have now proven that opposite sides (AD and CB) are congruent on a parallelogram.

Answer 2

Before you can use ASA, you need another pair of congruent angles. But you can use the same reasoning/logic you used to prove that first pair of angles were congruent

Answer 3

That's all that's missing? I thought of that, but must've forgotten to put it in. Whoops
Does it look find otherwise?

Answer 4

*fine

Answer 5

1st n 3rd pic not showing n everything @jim_thompson5910 said :)

Answer 6

@superdavesuper the links have a few extra characters at the end. Delete them and the links work fine

Answer 7

Yeah, the first and third won't show because of the symbols after the links in my essay.

Answer 8

So the other pair of congruent angles, according to the figures I'd drawn, would be DBC and ADB, correct?

Answer 9

That is correct.

Answer 10

Okay, so I've got everything now?
I'm just trying to be a perfectionist on this question.

Answer 11

Well, I have everything by adding that in on my essay.

Answer 12

yes I think that was the only thing missing really. Other than that, it looks great

Answer 13

probably stating the "obvious" DB=BD as it is common. Otherwise u are all good :)

Answer 14

oh true, BD = BD or DB = DB by the reflexive property

Answer 15

Would that go at the end, after I've seemingly proven that?

Answer 16

it would go before ASA is used

it's the "S" in ASA

Answer 17

Ah, okay. Thanks.

Answer 18

np