Question

in △abc and △def, ∠a ≅ ∠d and ∠b ≅ ∠e. what additional information is needed to prove that △abc ≅ △def by the asa congruence theorem? (1 point)

○ ab ≅ de

○ ∠c ≅ ∠f

○ bc ≅ ef

○ ac ≅ df

Explanation:

Step1: Recall ASA Congruence Theorem

The ASA (Angle - Side - Angle) Congruence Theorem 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: Identify given angles

We are given that $\angle A\cong\angle D$ and $\angle B\cong\angle E$. The included side between $\angle A$ and $\angle B$ in $\triangle ABC$ is $\overline{AB}$, and the included side between $\angle D$ and $\angle E$ in $\triangle DEF$ is $\overline{DE}$.

Step3: Determine needed information

To prove $\triangle ABC\cong\triangle DEF$ by ASA, we need $\overline{AB}\cong\overline{DE}$.

Answer:

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