Question

(b) problem 15: (first taught in lesson 34)
from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement.
given: ∠d ≅ ∠q, ∠c ≅ ∠p, (overline{de}) ≅ (overline{qn})
prove: △cde ≅ △pqn
a b c d e
angle - side - angle postulate

Explanation:

Step1: Identify given information

Given $\angle D\cong\angle Q$, $\angle C\cong\angle P$, $\overline{DE}\cong\overline{QN}$.

Step2: Recall congruence postulates

The Angle - Side - Angle (ASA) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step3: Match with ASA

In $\triangle CDE$ and $\triangle PQN$, $\overline{DE}$ is the side included between $\angle D$ and $\angle E$ (not given but can be deduced from triangle - angle sum), and in $\triangle PQN$, $\overline{QN}$ is the side included between $\angle Q$ and $\angle P$. Since two angles and the included side are congruent, we use ASA to prove $\triangle CDE\cong\triangle PQN$.

Answer:

A. Angle - Side - Angle Postulate