Chapter 4.1, Problem 11PSB

To determine

To Verify: $AB=DC$ .

Explanation of Solution

Given information: $AB=DC,AF=EC,BD\perp AF,BD\perp EC$ .

Formula Used: Congruency of triangles.

Verification:

  $\begin{array}{l}AB=DC,AF=EC,BD\perp AF,BD\perp EC(given)\\ \therefore \angle AFD={90}^{\circ }=\angle CEB\\ \therefore \Delta AFD\cong \Delta CEB(RHS)\\ \therefore FD=EB(CPCT)\\ \therefore FD-EF=EB-EF\\ \therefore DE=BF\\ \therefore \Delta AFB\cong \Delta CED(SAS)\\ \therefore AB=DC(CPCT)\end{array}$