Chapter 3.4, Problem 15PSC

To determine

To prove: Two given angles are congruent.

Answer to Problem 15PSC

  $\angle 1\text{ \& }\angle 2$ are congruent

Explanation of Solution

Given information :

Two-line segments are $\overline{\text{AB}}\text{ and }\overline{\text{AC}}$ Congruent

Two another line segment $\overline{\text{BD}}\text{ and }\overline{\text{CE}}$ are congruent.

Formula used:

Congruency means same size and same shape

Proof:

  $\begin{array}{l}\text{Since, it is give}\\ \overline{\text{AB}}\cong \overline{\text{AC}}\text{ and }\\ \overline{\text{BD}}\cong \overline{\text{CE}}\\ \therefore \overline{\text{AB}}\text{ = }\overline{\text{AC}}\text{ and }\overline{\text{BD}}\text{ = }\overline{\text{CE}}\mathrm{......}\left(i\right)\\ \left(\text{by definition of congruency}\right)\\ \text{In }\Delta \text{ABC,}\\ \overline{\text{AB}}\text{ = }\overline{\text{AC}}\mathrm{....}\text{from}\left(i\right)\\ \angle \text{ABC}=\angle \text{ACB, }\\ \left(\text{angles opposite to equal sides in }\Delta \text{ABC}\right)\\ \angle \text{1}=\angle \text{2}\\ \text{Hence proved}\end{array}$