Triangle ABC is congruent to triangle EDC because:
- Midpoint C makes AC and CE, BC and CD equal.
- Vertical angles ACB and ECD are equal.
- SAS congruence rule applies: two sides and an included angle (Side-Angle-Side) match in both triangles.
Therefore, they're completely overlapping mirror images of each other
Here's the proof:
1. Statement:
- Given: C is the midpoint of AE and BD.
- Prove: triangle ABC is congruent to triangle EDC.
2. Diagram: (Imagine a visual here)
- Draw a diagram with points A, B, C, D, and E arranged as described.
- Label C as the midpoint of AE and BD.
Connect points A, B, C, D, and E to form triangles ABC and EDC.
3. Proof:
- Segment AC is congruent to EC:
- C is the midpoint of AE, so AC = CE by definition of a midpoint.
- Segment BC is congruent to DC:
- C is the midpoint of BD, so BC = CD by definition of a midpoint.
- Angle ACB is congruent to angle ECD:
- Vertical angles are congruent, and ACB and ECD are vertical angles.
4. Conclusion:
By the Side-Angle-Side (SAS) Congruence Postulate:
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Therefore, triangle ABC is congruent to triangle EDC.
Visual explanation:
- The diagram visually demonstrates the congruent segments AC and CE, BC and CD, and the congruent angles ACB and ECD.
- It helps visualize the overlapping triangles and reinforces the SAS congruence.
The probable question can be: GIVEN: C is the midpoint of AE and of BD
PROVE: triangleABC = triangleEDC