Questions: Is there enough information to conclude that the two triangles are congruent? If so, which is the correct congruence statement? Yes; triangle ABC congruent to triangle ACD Yes; triangle ACB congruent to triangle ACD Yes; triangle CAB congruent to triangle DAC No; the triangles cannot be proven congruent.

Solution Steps

We are given triangle ABD with segment AC. We know that AB is congruent to AD (marked with single hash marks). We also know that AC is perpendicular to BD since angle ACB is a right angle (marked with a small square).

Since AC is perpendicular to BD, it forms right angles at C. Thus, angle ACB and angle ACD are both right angles, and therefore congruent. Side AC is shared by both triangles ABC and ACD, so AC is congruent to AC (reflexive property).

We have two pairs of congruent sides (AB ≅ AD and AC ≅ AC) and a pair of congruent angles (∠ACB ≅ ∠ACD) that are not between the two pairs of congruent sides. The congruence statements are written with corresponding vertices in the same order.

Final Answer