Question

use the two triangles below to answer the following questions.

enter a congruence statement about the two triangles.

to enter a congruence statement, type cong(triangle(vertices), triangle(vertices)). for instance, cong(triangle(pqr), triangle(xyz)) yields the statement $\triangle pqr \cong \triangle xyz$.

select the triangle congruency theorem that justifies your statement above.
\\( \circ \\) angle-angle-side triangle congruence (aas)
\\( \circ \\) side-angle-side triangle congruency (sas)
\\( \bullet \\) angle-side-angle triangle congruency (asa)

Explanation:

Step1: Identify Corresponding Angles and Sides

In $\triangle ABC$ and $\triangle EDF$:

• $\angle A = \angle E$ (marked equal angles).
• Side $AB = ED$ (marked equal sides).
• $\angle A = \angle E$, side between them (AB and ED) and $\angle A$ with $\angle C$ and $\angle E$ with $\angle D$: $\angle C = \angle D$ (marked equal angles). So the order of vertices should match corresponding angles and sides. So $\triangle ABC \cong \triangle EDF$ (by ASA as two angles and included side are equal).

Step2: Write Congruence Statement

Using the format, the congruence statement is $\text{cong(triangle(ABC), triangle(EDF))}$.

Answer:

$\text{cong(triangle(ABC), triangle(EDF))}$

For the theorem, since two angles and the included side are congruent, the justifying theorem is Angle - Side - Angle Triangle Congruency (ASA).