Questions: Determine whether the triangles are congruent. If so, name the postulate or theorem that justifies your answer. If not, explain.

Transcript text: Determine whether the triangles are congruent. If so, name the postulate or theorem that justifies your answer. If not, explain.

Solution

Solution Steps

Step 1: Identify the Given Information

The problem provides a diagram with two triangles, \( \triangle ABD \) and \( \triangle CDB \). The diagram shows that:

\( \angle ADB \) and \( \angle CDB \) are right angles.
\( AD \) is congruent to \( CD \) (marked with a single tick).
\( BD \) is a common side to both triangles.

Step 2: Determine Congruence Criteria

To determine if the triangles are congruent, we need to check if they satisfy any of the triangle congruence postulates (SSS, SAS, ASA, AAS, or HL).

Step 3: Apply the Hypotenuse-Leg (HL) Theorem

Since both triangles are right triangles, we can use the Hypotenuse-Leg (HL) Theorem, which states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Hypotenuse: \( AD \) is congruent to \( CD \).
Leg: \( BD \) is a common side.