In the image, the question asks which pair of overlapping triangles are congruent by the AAS (Angle-Angle-Side) criterion. Let's review each option:

• Option a: ΔADC ≅ ΔEBC

  • To check congruency by AAS, two angles and one side not between them should be congruent.
  • ΔADC and ΔEBC share angle D (right angle), but the other angles and sides must be compared to check this criterion.

• Option b: ΔABE ≅ ΔCDA

  • Similar to option a, we need to check if two angles and the non-included side are congruent between these two triangles.

• Option c: ΔABE ≅ ΔDEA

  • Again, angle comparisons will help determine if two angles and a side (not between them) are congruent.

• Option d: ΔADC ≅ ΔEDA

  • Here, checking for congruency by AAS is necessary for angles and side length between the two triangles.

To determine which pair satisfies the AAS condition, I will carefully analyze the triangle geometry and the placement of the right angles and shared sides. Based on the layout of the diagram, it seems that ΔADC ≅ ΔEDA (option d) would be the congruent pair by AAS.

Would you like me to go over the steps for checking this congruency further? Let me know if you need more details!

Here are a few related questions to explore:

1. What is the AAS congruence criterion in more detail?
2. How does the reflexive property of shared sides apply to congruence in triangles?
3. Can overlapping triangles also be congruent by SAS (Side-Angle-Side)?
4. What are the differences between AAS and ASA (Angle-Side-Angle)?
5. How does the Pythagorean Theorem help in proving congruence for right-angled triangles?

Tip: When using AAS, remember that the side must not be between the two angles; it's opposite them. This allows you to check triangle congruency by angles and a corresponding side.