Chapter 6, Problem 19CR

To determine

To prove : The congruency of $\angle B$ with respect to $\angle C$ .

Explanation of Solution

Given information : Here, we have given that $\overline{AC}\cong \overline{BD}$ and $\overline{AB}\cong \overline{CD}$

Proof: Construction: Join $\overline{BC}$

In $\Delta ABC$ and $\Delta DCB$

  $\overline{AB}\cong \overline{CD}$ (Given)

  $\overline{BC}\cong \overline{BC}$ (Common)

  $\overline{AC}\cong \overline{BD}$ (Given)

  $\Rightarrow \Delta ABC\cong \Delta DCB$ (By SSS Congruency Rule)

  $\therefore \angle B\cong \angle C$ (By Corresponding Part of Congruent Triangles)