The problem asks to determine the relationship between the two triangles and whether or not they can be proven congruent.

Analysis of the Triangles:

1. Marks on the Sides: Both triangles have one pair of corresponding sides marked as congruent (equal in length).
2. Right Angles: Each triangle has a right angle, indicating that the triangles share a common angle.

This setup suggests the Hypotenuse-Leg (HL) Congruence Theorem might apply. The HL theorem 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.

In this case:

• The marked side (a leg) is congruent in both triangles.
• The right angle provides the shared angle condition for the HL theorem to hold.

Thus, the two triangles are related by the Hypotenuse-Leg (HL) criterion, and they can be proven congruent.

Would you like further clarification on the HL theorem or any other aspects?

Related Questions:

1. What are the different congruence criteria for triangles (e.g., SSS, SAS, ASA)?
2. How does the Hypotenuse-Leg theorem differ from other triangle congruence theorems?
3. What conditions must be satisfied for two triangles to be congruent using the Side-Angle-Side (SAS) theorem?
4. Can triangles with only one pair of corresponding sides be congruent?
5. How can you prove triangle similarity if congruence is not possible?

Tip:

When dealing with right triangles, always consider the Hypotenuse-Leg (HL) theorem as a possible congruence shortcut if the right angle and one leg are given.