Help with number 22? **Proofs****21.** In square \( ABCD \), prove \( \triangle ADE \cong \triangle ABE \).*Diagram Description:* There is a square \( ABCD \) with diagonals \( AC \) and \( BD \) intersecting at point \( E \). Triangles \( ADE \) and \( ABE \) are formed by this intersection.---**22.** In parallelogram \( ABCD \), \( E \) and \( F \) are the midpoints of \( \overline{AB} \) and \( \overline{CD} \), respectively. Prove that \( AECF \) is a parallelogram.

Answered: Image /qna-images/answer/8e0e8523-a0e9-493c-9e1a-9a04da959376.jpgGiven that ABCD is a parallelogram having AB=CD Also, E and F are midpoints of sides AB and CD respectively. Now, If E is the midpoint of AB then we have, AE=EB .....(1) Also, F is the midpoint of CD then we have, DF=FC ......(2) Since AB=CD ....(3) Then from equation (1), (2), and (3) We have, AE=FC Also, AB||CD by which we can say that AE||FC By definition: When opposite sides are equal and parallel then the quadrilateral is known as Parallelogram. Hence, AECF is a Parallelogram. Hence Proved.