Chapter 4.3, Problem 7ST1

To determine

Toprove: $\angle 1\cong \angle 2$.

Explanation of Solution

Given information :

If $\overline{CD}\cong \overline{AB};\overline{CB}\cong \overline{AD}$ and

  

Proof: Since $\overline{CD}\cong \overline{AB};\overline{CB}\cong \overline{AD}$ and $BD\cong BD$ as common side

By SSS theorem, the given two triangles are congruent.

Thus, $\Delta ADB\cong \Delta CBD$

  $\Rightarrow$ The pairs of sides and angles of two triangles are equal in measurement

Hence, $\angle 1\cong \angle 2$