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Is this SSS SAS ASA AAS HL or not congruent? And don't assume any measurements

The image shows two triangles, \( \triangle ABE \) and \( \triangle CDE \), which share a common vertex at point \( E \). The markings on the diagram indicate the following:

1. \( AB = CD \) (shown by the single tick marks on these sides).
2. \( \angle ABE = \angle CDE \) (the angles are marked as congruent at points \( B \) and \( C \)).
3. The two triangles share the side \( BE = DE \), implying that \( BE = DE \).

Given this information, the triangles can be proven congruent using the **SAS (Side-Angle-Side)** criterion. This is because:
- Two sides (\( AB = CD \) and \( BE = DE \)) are congruent.
- The angle between these sides (\( \angle ABE = \angle CDE \)) is also congruent.

Thus, the two triangles \( \triangle ABE \) and \( \triangle CDE \) are congruent by the **SAS** postulate.

Would you like further explanation or have any questions?

Here are some related questions for further exploration:

1. What is the difference between SAS and SSS congruence postulates?
2. How would you use the ASA criterion to prove triangle congruence?
3. Can triangles be congruent if only two angles are known to be congruent?
4. What role does the included angle play in the SAS postulate?
5. How can we prove triangle congruence in a right triangle using the Hypotenuse-Leg (HL) criterion?

**Tip:** Always check for congruent sides and angles carefully. The position of the included angle is crucial for the SAS criterion.

Is this SSS, SAS, ASA, AAS, HL or not congruent? And don't assume any measurements.

This problem demonstrates how to determine triangle congruence using the SAS criterion. The two triangles share a side and have congruent angles, proving them congruent by the SAS postulate. Suitable for students in Grades 8-10.

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