Chapter 15.3, Problem 21PSC

To determine

To Find: The correct statement for the given figure.

Answer to Problem 21PSC

  $a$

Explanation of Solution

Given:

  $\begin{array}{l}ABCD\text{ is a square}\\ \overline{AF}\perp \overline{DE}\\ \overline{AE}\cong \overline{BF}\end{array}$

  

Formula Used:

The Hinge Theorem: It states that if two sides of two triangles are congruent and angle of one is greater than the angle of second then the third side of the triangle will be greater than the another.

Calculation:

  

  $\begin{array}{l}\text{⇒}\Delta AED\approx \Delta FBA\\ \text{⇒}DE=AB\\ \text{⇒}AF=AD\\ \text{⇒}AD>DE\\ \text{⇒}AF>DE\end{array}$

Conclusion:

Thus from the calculation it is proved that option a is correct that is $AF>DE$