Question

is there enough information to conclude that the two triangles are congruent? if so, which is the correct congruence statement?
yes, △cab≅△dac
yes, △acb≅△acd
yes, △abc≅△acd
no, the triangles cannot be proven congruent.

Explanation:

Step1: Identify equal - sides

We see that \(AB = AD\) (marked with the same number of dashes) and \(AC\) is common to both \(\triangle ABC\) and \(\triangle ADC\). Also, \(\angle ACB=\angle ACD = 90^{\circ}\).

Step2: Apply congruence criterion

By the Hypotenuse - Leg (HL) congruence criterion (in right - triangles, if the hypotenuse and one leg are equal), \(\triangle ABC\cong\triangle ADC\). The correct congruence statement should have the vertices in the correct corresponding order. The correct congruence statement is \(\triangle ACB\cong\triangle ACD\) as the right - angles are at \(C\), and the equal sides match up correctly.

Answer:

Yes, \(\triangle ACB\cong\triangle ACD\)