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Can you determine whether these two triangles are classified as SSS SAS ASA AAS HL or not congruent? Also don’t assume any measurements, only go by and determine measurements based on the tick marks and angle arcs that are given. And always start with ABC as the first shape.

Let's analyze the two triangles in the image, specifically \( \triangle ABC \) and \( \triangle CDE \), based on the provided tick marks and angle arcs.

### Step-by-Step Analysis:

1. **Sides (Tick Marks):**
   - \( AB \) is marked with one tick, indicating that it's congruent to \( DE \), which also has one tick.
   - \( BC \) is marked with two ticks, indicating that it's congruent to \( CE \), which also has two ticks.

2. **Angles (Arc Marks):**
   - The angle at \( C \) is marked with two arcs, which means \( \angle ACB \) is congruent to \( \angle DCE \).

### Conclusion:
Based on the congruence of two sides and the included angle between them, we can classify the triangles as **SAS** (Side-Angle-Side) congruent.

Would you like more details or have any questions?

Here are 5 related questions to further explore:
1. Can you prove the triangles are congruent using the Law of Cosines?
2. What would happen if only one pair of sides were marked as congruent?
3. How does the classification change if the included angle wasn't marked?
4. What other methods can be used to prove triangle congruence if only angles are given?
5. How can we use triangle congruence to prove the lengths of sides?

**Tip:** Always check for included angles when using the SAS criterion!

Can you determine whether these two triangles are classified as SSS, SAS, ASA, AAS, HL, or not congruent? Also, don’t assume any measurements, only go by and determine measurements based on the tick marks and angle arcs that are given. Always start with ABC as the first shape.

This problem involves determining triangle congruence based on tick marks and angle arcs for triangles ABC and CDE. Using the SAS criterion, the congruence of two sides and the included angle proves that the triangles are congruent. Suitable for students in Grades 8-10.

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