Subjects geometry

Triangle Congruency

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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.