Chapter 4.4, Problem 4CYP

To determine

To prove: $\angle LNM\cong \angle LNP$

Explanation of Solution

Given information: $\overline{MN}\cong \overline{PN}$ and $\overline{LM}\cong \overline{LP}$

  

Proof: The two columns proof has been given below.

  $\begin{array}{cc}\text{Statements}& \text{Reasons}\\ \begin{array}{l}\overline{MN}\cong \overline{PN}\\ \overline{LM}\cong \overline{LP}\\ \angle MNL\cong \angle PNL\\ \overline{LN}=\overline{NL}\\ \Delta LNM\cong \Delta LNP\\ \angle LNM\cong \angle LNP\end{array}& \begin{array}{l}\text{Given}\\ \text{Given}\\ \text{Congurent sides}\\ \text{Reflexive property}\\ \text{Congruent triangles}\\ \text{By side-side-side congruence postulate}\end{array}\end{array}$