Chapter 3.2, Problem 20PSB

To determine

Reasoning has to be provided for the statements. Also, congruency of $\Delta EMB\cong \Delta EMC$ has to be proved

Answer to Problem 20PSB

The congruency is proved in statement $5$

Explanation of Solution

Given information : The following information has been given

M is midpoint of BC

  $\angle 1\cong \angle 2$

  $\overrightarrow{BE}\cong \overrightarrow{CE}$

The reasons for the statements will be as follows

  $1$ . Statement is given as information

  $2$ . $\angle 1$ and $\angle 3$ form a straight line. Thus, they are supplementary

  $3$ . $\angle 2$ and $\angle 4$ form a straight line. Thus, they are supplementary

  $4$ . As M is midpoint of BC, thus $\overrightarrow{MB}\cong \overrightarrow{MC}$

  $5$ . We have EM as a common chord, $\overrightarrow{MB}\cong \overrightarrow{MC}$ , and a common chord EM. Hence, by SSS property we can say that $\Delta EMB\cong \Delta EMC$

Thus, the congruency is also proven in statement $5$

Hence, required solutions are proved