true or false

Question

if the opposite sides of quadralateral are equal, it is a parallelogram

Answer 1

It is true.

 

This will be a challenge to explain without the use of diagrams!! :)

 

Draw quadrilateral ABCD with AB=CD and BC=AD

 

Since AB=CD (given) and BC=AD (given) and AC=CA (reflexive property), ΔABC ≅ ΔCDA by SSS.

 

Then, you can prove angles are congruent through CPCTC and some simple algebra.

 

Once you establish that opposite angles are congruent, you can use alternate interior angles to show that the opposite sides are parallel, thus making ABCD a parallelogram.