Chapter 5.1, Problem 1PSA

To determine

To Prove: $\overline{BC}\cancel{\cong }\overline{DC}$ .

Explanation of Solution

Given:

  

  $\overline{AB}\cong \overline{AD},\angle BAC\cancel{\cong }\angle DAC$

Concept Used:

Two line segments are said to be congruent if they are of the same measure.

Proof:

Here, we have

  $\begin{array}{l}\text{In }\Delta ABC\text{and }\Delta ABC\\ \overline{AB}\cong \overline{AD}\left(\text{Given}\right)\\ \overline{AC}\cong \overline{AC}\left(\because \text{Common side}\right)\\ \angle BAC\cancel{\cong }\angle DAC\left(\text{Given}\right)\\ \Rightarrow \Delta ABC\cancel{\cong }\Delta ABC\\ \therefore \overline{BC}\cancel{\cong }\overline{DC}\end{array}$