Question

The figure below shows a quadrilateral ABCD. Sides AB and DC are equal and parallel:


(Picture in replies)

A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram:

Side AB is equal to side DC, and DB is the side common to triangles ABD and CDB. Therefore, the triangles ABD and CDB are congruent by SAS postulate. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB ________. Therefore, AD is parallel and equal to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.

Which phrase best completes the student's proof?

are congruent by the AAS postulate
are congruent by the ASA postulate
form a pair of alternate interior angles that are congruent
form a pair of vertical angles that are congruent

Answer 1

We can remove options A and B from the list, now what do you think the answer is and feel free to look up the definition of alternate interior angles and vertical angles.

Answer 2

is it C?

Answer 3

that looks like it would make sense but I dont know...

Answer 4

Yes, you're correct! Sorry I was AFK

Answer 5

Could I get a medal, please?

Answer 6

Gracias :)