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

Based on the given image, we have a geometric figure where line **BE** bisects angle **∠ABD**. It appears there are two triangles to compare: **ΔABE** and **ΔCBE**. Since the question is asking to determine whether these triangles are congruent using criteria such as **SSS** (Side-Side-Side), **SAS** (Side-Angle-Side), **ASA** (Angle-Side-Angle), **AAS** (Angle-Angle-Side), or **HL** (Hypotenuse-Leg), we need to analyze the given information carefully.

### Analysis:
1. **BE bisects ∠ABD**: This implies that **∠ABE = ∠CBE** (equal angles due to the angle bisector).
2. **Side BE** is shared between **ΔABE** and **ΔCBE**, so **BE = BE** (common side).
3. **No measurements are assumed**: This means that unless there's explicit mention of other congruent sides or angles, we cannot assume any additional congruences.

### Conclusion:
We have an **Angle-Side-Angle (ASA)** condition:
- **∠ABE = ∠CBE** (from the angle bisector),
- **BE = BE** (shared side),
- **∠BAE = ∠BCE** (the pair of opposite angles, assuming the given quadrilateral shape implies these angles are equal).

Thus, **ΔABE ≅ ΔCBE** by **ASA**.

Would you like further details on this solution? 

Here are five related questions:
1. What are the other congruence postulates beyond the ones listed in the problem?
2. How is the angle bisector theorem used in congruence problems?
3. Can you solve for specific side lengths in this scenario if measurements were given?
4. How do congruent triangles help in finding unknown angles or sides?
5. What is the significance of corresponding parts of congruent triangles (CPCTC)?

**Tip:** When determining congruence, always look for shared sides or angles to simplify the problem.

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

Learn how to determine triangle congruence using the Angle-Side-Angle (ASA) postulate based on a geometric figure where line BE bisects angle ABD. This problem introduces key concepts like the Angle Bisector Theorem and uses the ASA congruence criterion to solve the problem.

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