Triangle Congruency
1. **Problem Statement:**
We analyze Diagram B and solve the questions: identify triangles, check for congruency, complete the transformation table, and discuss similarity and congruency conditions.
2. **Identifying Triangles (2.1.1):**
- In Diagram B, triangles visible are $\triangle ACB$ and $\triangle DEC$.
3. **Checking Congruence (2.1.2):**
- To determine if $\triangle ACB$ and $\triangle DEC$ are congruent, check side lengths and angles.
- If $AC = DE$, $CB = EC$, and the included angle $\angle ACB = \angle DEC$, the triangles are congruent by SAS (Side-Angle-Side).
- Without measurements from the diagram, congruency cannot be confirmed. If these conditions hold, triangles are congruent.
4. **Completing the Transformations Table (2.2):**
| Congruent figures | Translation | Reflection | Rotation | Enlargement |
|-------------------|-------------|------------|----------|-------------|
| Yes | Yes | Yes | Yes | No |
- Translation, reflection, and rotation produce congruent figures (same size and shape).
- Enlargement produces similar figures, which may not be congruent (changes size).
5. **Transformations Producing Similar but Not Congruent Figures (2.2.1):**
- Enlargement produces similar figures that are not congruent.
- It changes size but maintains the shape.
6. **Conditions for Congruency under Enlargement (2.2.2):**
- Figures are congruent only if the enlargement scale factor is 1, meaning size does not change.
**Final Answers:**
- 2.1.1 Triangles are $\triangle ACB$ and $\triangle DEC$.
- 2.1.2 Triangles are congruent if SAS holds: $AC=DE$, $CB=EC$, and $\angle ACB = \angle DEC$.
- 2.2 Transformation table completed.
- 2.2.1 Enlargement produces similar but not congruent figures.
- 2.2.2 Congruency under enlargement when scale factor = 1.