Chapter 6, Problem 16CR

To determine

To prove : ABCD is a parallelogram

Explanation of Solution

Given information : Here, we have given that A, B, C and D lie in m, FBCE is a parallelogram, $\overline{FE}\parallel \overline{AD}$ and $\overline{AD}\cong \overline{BC}$ .

Formula used: If any one pair of sides of quadrilateral becomes equal and parallel, then that quadrilateral is said to be a parallelogram.

Proof: As, FBCE is a parallelogram,

  $\Rightarrow \overline{FE}\parallel \overline{BC}$

Now, as it given that $\overline{FE}\parallel \overline{AD}$ and it is proved that $\overline{FE}\parallel \overline{BC}$ ,

  $\Rightarrow \overline{AD}\parallel \overline{BC}$

As, $\overline{AD}\cong \overline{BC}$ and $\overline{AD}\parallel \overline{BC}$ ,

  $\Rightarrow$ ABCD is a parallelogram