Chapter 1.7, Problem 12PSB

To determine

To Prove: Whether or not the conclusion deduced for question is true

Answer to Problem 12PSB

The deduced conclusion is true;

In $\Delta ABC$ , $\overrightarrow{BC}\cong \overrightarrow{AC}$

Explanation of Solution

Given information: The following two statements are given:

Statement $1$ : If two angles of a triangle are congruent, then the sides opposite them are congruent

Statement $2$ : In $\Delta ABC$ , $\angle A\cong \angle B$

Formula used: the formula for congruency of sides has been used

Proof: Using the argument of statement $1$ in statement $2$ , we can say that the sides opposite to the $\angle A$ and $\angle B$ will be congruent

Thus, the sides opposite to these angles are:

  $\angle A\to \overrightarrow{BC}$

  $\angle B\to \overrightarrow{AC}$

And,

  $\angle A\cong \angle B$

  $\to \overrightarrow{BC}\cong \overrightarrow{AC}$

Hence, proved, that the sides BC and AC are congruent