Chapter 4.5, Problem 27STP

To determine

To evaluate: the theorem that could be used to prove $\Delta ABC\cong \Delta DBC$ .

Answer to Problem 27STP

Option B is correct.

Explanation of Solution

Given:

It is given that $\overline{BC}$ is perpendicular to $\overline{AD}$ ; $\angle 1\cong \angle 2$

  

In $\Delta ABC$ and $\Delta DBC$

  $\begin{array}{l}BC=BC\\ \angle 1=\angle 2\\ \angle BCA=\angle BCD\mathrm{.....}\left({90}^o\right)\end{array}$

So,

By ASA criterion,

  $\Delta ABC\cong \Delta DBC$

So, ASA criterion is right answer.

Hence, option B is correct.