Chapter 7, Problem 1RP

To determine

To prove : The congruency of $\angle A\cong \angle BDC$

Explanation of Solution

Given information : The following information has been given

  $\angle DBC\cong \angle E$

Formula used : The sum of the measures of angles in any triangle is ${180}^0$

Proof : We compare the triangles CDB and CEA. Thus, we have

  $\angle C$ is the common angle

Now, we know that the other two angles of both triangles will sum up to equal values because their sum is constant. Hence, we get

  $\angle A+\angle E\cong \angle BDC+\angle DBC$

Now, we know that $\angle DBC\cong \angle E$ . Thus, substituting its value, we get

  $\angle A\cong \angle BDC$