Chapter 4.4, Problem 3CYU

To determine

To prove: $\Delta LMP\cong \Delta NMO$

Explanation of Solution

Given information: $\overline{LP}\cong \overline{NO},\angle LPM\cong \angle NOM$ and $\Delta MOP$ is equilateral.

  

Proof: It is given that $\overline{LP}\cong \overline{NO},\angle LPM\cong \angle NOM$ and $\Delta MOP$ is an equilateral triangle. Thus, by definition of equilateral triangle, $\overline{MO}\cong \overline{MP}$ . So, two sides and the included angle of $\Delta LMP$ are congruent to two sides and the included angle of $\Delta NMO$ . Therefore, by the Side-Angle-Side congruence postulate, $\Delta LMP\cong \Delta NMO$