Question

7. Triangle CDA is the image of triangle ABC after a 180° rotation around the midpointof segment AC. Triangle ECB is the image of triangle ABC after a 180° rotationaround the midpoint of segment BC.DсEa. Explain why ABCD and ABEC areparallelograms.ABYour answer

Answer 1

`\begin{gathered} 1.CE=AB,CE\parallel AB \\ 2.DC=AB,DC\parallel AB \\ 3.DA=CB,DA\parallel CB \\ 4.AC=BE,AC\parallel BE \end{gathered}`

By definition a parallelogram:

* Its opposite sides are equal in length

* Its opposite sides are parallel.

Since the figures ABCD and ABEC satisfy those properties, we can conclude that they are parallelograms