Question

4-6: lesson quiz (exit ticket) in the figure shown, what additional information is needed to show that △ abc ≅ △ def by asa? a. m∠c b. \\(\overline{ab} \cong \overline{de}\\) c. m∠f d. \\(\overline{bc} \cong \overline{ef}\\)

Explanation:

Step1: Recall ASA Criterion

ASA (Angle - Side - Angle) congruence criterion 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.

Step2: Analyze Given Angles

In $\triangle ABC$ and $\triangle DEF$, we can see that $\angle B\cong\angle E$ (marked angles) and $\angle A$ and $\angle D$ are right angles (so $\angle A\cong\angle D$). For ASA, we need the included side between the two angles. The included side between $\angle A$ and $\angle B$ in $\triangle ABC$ is $AB$, and the included side between $\angle D$ and $\angle E$ in $\triangle DEF$ is $DE$. So we need $AB\cong DE$ to apply ASA.

Let's check other options:

• Option A: Knowing $m\angle C$ doesn't help with ASA directly as we need a side.
• Option C: Knowing $m\angle F$ doesn't give us the included side.
• Option D: $BC$ and $EF$ are not included sides for the given angles.

Answer:

B. $\overline{AB}\cong\overline{DE}$