Question

Prove that the opposite angles of a parallelogram are congruent.
http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_1004_04/image0154e985306.gif

Answer 1

@J.L. take triangle
ABC and ADC
here we know
that
AC= AC ( common side)
AB= CD ( opposite sides of a parallelogram are equal)
BC=AD (-same-)
so triangle ABC= triangle ADC
do you get this?

Answer 2

I think I have to write a paragraph proof. I thought we would write something about the vertical angle theorem...

Answer 3

So would I start the proof as: It is given that quadrilateral ABCD is a parallelogram. Using the Reflexive Property, we know that line AC is congruent to line AC.

Answer 4

yeah, doing good:)

Answer 5

Line AB is congruent to line CD because opposite sides of a parallelogram are equal. Line BC is equal to line AD because both pairs of opposite sides of a parallelogram are congruent and parallel. Therefore, triangle ABC is congruent to triangle ADC.

Answer 6

@ash2326

Answer 7

yeah you're correct:D

Answer 8

So the last sentence would be: opposite angles of a parallelogram are congruent using CPCTC?

Answer 9

yeah:D angle ABC= angle ADC using CPCTC

Answer 10

Thank you so much!

Answer 11

welcome:D