Question

problem 12: (lesson 34)
from this given statement, select the definition, property, postulate, or theorem that justifies the prove statement.
given: $overline{ab}congoverline{tp}$, $angle acongangle t$, $angle abpcongangle tpu$
prove: $\triangle apbcong\triangle tup$

Explanation:

Step1: Identify given congruences

We are given $\overline{AB}\cong\overline{TP}$, $\angle A\cong\angle T$, and $\angle ABP\cong\angle TPU$.

Step2: Recall congruence postulates

The 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 $\triangle APB$ and $\triangle TUP$, $\overline{AB}$ is the included side between $\angle A$ and $\angle ABP$, and $\overline{TP}$ is the included side between $\angle T$ and $\angle TPU$. Since the two - angle and one - side pairs are congruent as given, by the ASA postulate, $\triangle APB\cong\triangle TUP$.

Answer:

The Angle - Side - Angle (ASA) Postulate.