Question

hello can you recheck to see if am right. please. I say A Because they are parallelogram and both have a pair of parallel lines

Answer 1

By definition, a parallelogram is a four-sided plane figure with opposite sides parallel. To prove that ABCD and ABEC are parallelograms, we need to confirm that AB is parallel to CD and CE, AD is parallel to BC, and AC is parallel to BE.

Since ΔCDA is the triangle ΔABC rotated 180º, The side CD is a rotation of 180º of the corresponding side AB. When a segment is rotated by 180º, it keeps the same "inclination"(the same slope), and if two segments have the same slope they are parallel, therefore

`AB\parallel CD`

The same argument can be used to prove that

`\begin{gathered} AB\parallel CE \\ AD\parallel BC \\ AC\parallel BE \end{gathered}`

Thus,

ABCD and ABEC are parallelograms.