Question

line segments ad and be intersect at c, and triangles abc and dec are formed. they have the following characteristics:
∠acb and ∠dce are vertical angles
∠b ≅ ∠e
\overline{bc} ≅ \overline{ec}
which congruence theorem can be used to prove △abc ≅ △dec?
○ hl
○ asa
○ sss
○ sas

Explanation:

Step1: Recall the ASA congruence theorem

ASA (Angle - Side - Angle) 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 the angles and side in the given triangles

We know that \(\angle ACB\cong\angle DCE\) (vertical angles are congruent), \(\angle B\cong\angle E\), and \(BC\cong EC\). The side \(BC\) (in \(\triangle ABC\)) and \(EC\) (in \(\triangle DEC\)) is the included side between the pairs of congruent angles \(\angle B\) and \(\angle ACB\) (in \(\triangle ABC\)) and \(\angle E\) and \(\angle DCE\) (in \(\triangle DEC\)).

Answer:

ASA