Question

Write an indirect proof to show that opposite angles of a parallelogram are congruent. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted. Help please I don't know how to do this at all !!

Answer 1

Please!!!! I will fan & medal !!!

Answer 2

@ganeshie8

Answer 3

@studygurl14

Answer 4

@acarpenter2

Answer 5

We want to prove that \( \bf \angle A = \angle C~ and ~ \angle B = \angle D \).

Assume the opposite \( \bf \angle A \neq\ \angle C. \)

Can you derive a contradiction?

Answer 6

If A is not equal to C then they are also not equal to B & D ?

Answer 7

may be you need to extend two parallel line to use parallel lines and transverse

Answer 8

to arrive at contradiction

Answer 9

We are given from the figure that \( \bf AB \parallel CD ~and~ BC \parallel AD\).

Answer 10

Okay , I get what your saying but i don't understand how to contradict it .

Answer 11

Because BC is parallel to AD, angle C and D are supplementary (they are same side interior angles ) .
Similarly angle A and angle D are supplementary

Answer 12

angles which are supplementary to the same or congruent angles are congruent themselves. and thats a contradiction, since we assumed A is not equal to D

Answer 13

I'm sorry, if I'm not saying much im trying to understand I ... Sooooo that's how I contradict it ? The BC is parallel to AD thing

Answer 14

Do you agree that:
\( \bf BC \parallel AD\), and the two lines are cut by transversal CD,
therefore \(~ \bf \angle C + \angle D = 180 \).

Answer 15

Yes I do , I kinda see the parallel thing now.

Answer 16

so I would put to assume the negative first off negative Because BC is parallel to AD, angle C and D are supplementary (they are same side interior angles ) .
Similarly angle A and angle D are supplementary

Answer 17

so you are correct.

Answer 18

Oh okay , I see how you did that !!

Answer 19

Oh okay , I kinda see how we got to that!! Wow!

Answer 20

We want to prove that <A = <C and <B = <D
Proof:
Assume the negation. That <A is not equal to <C.

Then, because BC is parallel to AD with transversal CD, angle C and D are supplementary (they are same side interior angles ) .

Because AB is parallel to CD with transversal AD, angles A and D are supplementary.

Since <C is supplementary to <D and <A is supplementary to <D , that implies <A and <C are equal (because angles supplementary to the same angle are congruent.)

Now we have <A = <C and <A \( \neq\) <C.
Contradiction

Answer 21

also you can label the theorems that you used. same side interior angles are supplementary, and angles supp. to same angle are congruent

Answer 22

I got it now . Thank youu sooooo much for your help!!!