Question

Prove that the opposite angles of a parallelogram are congruent.

Answer 1

@satellite73 @amistre64 @jim_thompson5910

Answer 2

If we wanted to prove <1 = <3, then you would have to prove that triangles BAD and DCB are congruent

Answer 3

whats the proof then?

Answer 4

To do this, you use the idea that BD = BD (reflexive property), BC = AD (opposite sides of parallelogram are equal), and BA = CD (opposite sides of parallelogram are equal)

Answer 5

then you use the SSS property of congruence

Answer 6

So the basic proof outline is:

BD = BD (reflexive property)
BC = AD (opposite sides of parallelogram are equal)
BA = CD (opposite sides of parallelogram are equal)

These three facts lead to the fact that triangles BAD and DCB are congruent

By the CPCTC property, angle 1 and angle 3 are congruent

Answer 7

Note: CPCTC stands for "corresponding parts of congruent triangles are congruent"

Answer 8

Then use this idea to show that angles 2 and 4 are congruent