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

The given triangle diagram shows that:

1. \( BD \) bisects \( AE \), which suggests that segments \( AB \) and \( ED \) are equal in length. This is indicated by the two small markings on each of these segments.
2. \( \angle ACB \) and \( \angle ECD \) are right angles (indicated by the right angle symbol).
3. Segment \( AC \) is equal to segment \( EC \), as indicated by the single marking on both of these segments.

Since we are not given any specific measurements but can rely on the geometrical properties provided, we can assess whether the triangles \( \triangle ABC \) and \( \triangle EDC \) are congruent using the information at hand:

- **Right Angle**: \( \angle ACB = \angle ECD = 90^\circ \) (these are given right angles).
- **Hypotenuse**: \( AC = EC \), as indicated by the equal markings on these sides.
- **One leg**: \( AB = ED \), because \( BD \) bisects \( AE \).

This situation satisfies the **Hypotenuse-Leg (HL) Theorem** for right triangles, which states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, the two triangles are congruent.

Thus, the triangles are congruent by the **HL (Hypotenuse-Leg)** theorem.

Would you like any further details or explanations on this?

Here are 5 related questions:
1. What is the HL (Hypotenuse-Leg) theorem in detail?
2. Can the SSS or SAS theorem apply in this case?
3. How do we determine whether a bisector creates congruent segments in general?
4. What other methods are there to prove triangle congruence?
5. How can the Pythagorean Theorem help verify triangle congruence in right triangles?

**Tip:** Always check if the triangles you're working with are right triangles before applying the HL theorem!

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

Explore how triangles ABC and EDC are congruent using the Hypotenuse-Leg (HL) Theorem. The problem includes a bisector, right angles, and congruent segments, making it a perfect example for students in Grades 8-10.

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