The given diagram shows two right-angled triangles, $\triangle ABC$ and $\triangle DEF$, with congruent right angles marked and one pair of corresponding sides marked as equal in length.

For two triangles to be congruent, certain conditions must be met. The most common conditions for triangle congruence are:

1. Side-Side-Side (SSS): All three sides of one triangle are congruent to the corresponding three sides of the other triangle.
2. Side-Angle-Side (SAS): Two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle.
3. Angle-Side-Angle (ASA): Two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle.
4. Hypotenuse-Leg (HL): For right triangles, if the hypotenuse and one leg of one triangle are congruent to the corresponding parts of another triangle.

Analysis:

In the diagram:

• Both triangles are right triangles (90° angles marked).
• One pair of sides (the legs along the horizontal) is marked as equal, indicating that $AC = DF$.

However, there isn't enough information about the other sides (hypotenuses or vertical legs) to confirm if they are congruent. Without knowing the lengths of these sides, we cannot confirm congruence under the Hypotenuse-Leg (HL) condition or any other condition.

Thus, the triangles cannot be definitively proven to be congruent with the information provided.

Correct answer: B. False

Would you like more details or have any questions?

Here are 5 related questions to deepen understanding:

1. What are the five triangle congruence criteria?
2. How does the Hypotenuse-Leg (HL) theorem apply to right triangles?
3. How can you determine congruence using only angles and one side?
4. What role does similarity play in triangle geometry compared to congruence?
5. How can transformations like reflections and translations show triangle congruence?

Tip: Always check for matching sides or angles in corresponding parts of triangles when determining congruence.