Chapter 4.5, Problem 6PPS

To determine

To prove:

  $\Delta ECB\cong \Delta ECD$ for the following figure in the form of the paragraph:

  

Explanation of Solution

Given information:

  $\overline{CE}$ bisects $BED$

Right angles: $\angle BCE$ and $\angle ECD$

Proof:

From the given figure:

  

Since all right angles are congruent, therefore $\angle BCE\cong \angle ECD$ . According to the definition of angle bisector $\angle BCE\cong \angle DEC$ . According to the reflexive property the congruent segments are $EC\cong CE$ . Therefore, use the angle side angle (ASA) congruence postulate gets that: $\Delta ECB\cong \Delta ECD$

Hence proved.