Thread: Parallelograms & Parallel lines

In the image attached, triangle ABC is congruent to triangle A'B'C' & AB is parallel to A'B' & BC is parallel to B'C'. How do I show that

1. AA'B'B is a parallelogram
2. BB'C'C is a parallelogram
3. Is AA' parallel to CC'. Why?
4. Is AA'C'C a parallelogram?
5. Is AC parallel to A'C'? Why?

I have got the first 2 but can't get the 3rd one. Can someone please help me with the 3rd one?

Thanks,

Ron

I don't see any images.

Originally Posted by dwsmith

I don't see any images.

Sorry forgot to attach the image....

Since ABC and A'B'C are congruent, the length of AB=A'B' and the same for the other sides. We know AB and A'B' are parallel. Therefore, AA' and BB' are parallel.

If we have two parallel equal length sides and connect them, those 2 sides will be parallel and equal length. This should answer why opposite sides are parallel.