Question

identify the correct triangle congruence theorem.
sss
sas
hl
asa

Explanation:

Step1: Analyze the given information

We have two triangles \(\triangle ABC\) and \(\triangle DEC\). We know that \(AC = DC\) (marked with one cross), \(\angle A=\angle D\) (marked with one tick), and \(\angle ACB=\angle DCE\) (vertical angles are equal).

Step2: Recall the triangle - congruence theorems

• SSS (Side - Side - Side): Requires three pairs of equal sides.
• SAS (Side - Angle - Side): Requires two pairs of equal sides and the included angle.
• HL (Hypotenuse - Leg): For right - angled triangles.
• ASA (Angle - Side - Angle): Requires two pairs of equal angles and the included side.

In our case, we have two angles (\(\angle A=\angle D\) and \(\angle ACB = \angle DCE\)) and the included side (\(AC = DC\)).

Answer:

ASA