Question

The figure below shows a parallelogram ABCD. Side AB is parallel to side DC and side AD is parallel to side BC:

A student wrote the following sentences to prove that parallelogram ABCD has two pairs of opposite sides equal:

For triangles ABD and CDB, alternate interior angle ABD is congruent to angle CDB because AB and DC are parallel lines. Similarly, alternate interior angle ADB is equal to angle CBD because AD and BC are parallel lines. DB is equal to DB by reflexive property. Therefore, triangles ABD and CDB are congruent by SAS postulate. Therefore, AB is congruent to DC and AD is

Answer 1

Congruent to BC by CPCTC.

Answer 2

@tinybookworm

Answer 3

Yes? What is the question?

Answer 4

I need to upload a picture gimme one second.

Answer 5

Here we go!

Answer 6

Also the options..
Angle ADB is congruent to angle CBD because they are vertical angles.
Angle ADB is congruent to angle CBD because they are corresponding angles.
Triangles ABD and CDB are congruent by SSS postulate.
Triangles ABD and CDB are congruent by SAS postulate.

Answer 7

Because ABCD is a parallelogram, AD = CB and AB = CD. Two triangle has the same side DB so ...

Answer 8

Would it be option 2?

Answer 9

No. B only consider about the angles, not the sides

Answer 10

So would it be D?

Answer 11

Side angle side postulate.

Answer 12

No. Ok, AD = BC AB = CD and BD = BD

Answer 13

Sorry I'm not with it, I had a nosebleed in my sleep then I woke up with one. Been dizzy ever since.
So would it be option 3?

Answer 14

I am sorry. Yes, C is correct

Answer 15

Thanks for the help! Now I can move on.

Answer 16

You are welcome