Question

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

Answer 1

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

Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle CDB, are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and BCD 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 which are congruent

Answer 2

do you have any opinion ?

Answer 3

i was thinking that it would be the ASA postulate

Answer 4

how are these angles of ADB and DBC ?

Answer 5

there congruent, right?

Answer 6

yes congruent - right

Answer 7

are alternate ?

Answer 8

and interior are ?

Answer 9

yes? they are opposite of each other, but im not sure about interior

Answer 10

why not ? not are interior of this quadrilateral ?

Answer 11

oh yeah, they are

Answer 12

so than what will be the right choice answer ?

Answer 13

C

Answer 14

right?

Answer 15

yes exactly

do you understand it now ?

Answer 16

yes, thank you.
Can u help me with a few more?

Answer 17

please post on the open questions column and try tagging me there

Answer 18

ok, thank you

Answer 19

yw

was my pleasure

good luck

bye bye