Discovering the Magic of SSS and SAS Congruence in Triangles
- Ensure you know the lengths of all three sides of both triangles.
- Compare each corresponding side.
- If all three sides in one triangle are equal in length to the three sides of the other triangle, the two triangles are congruent.
- Ensure you know the lengths of two sides and the magnitude of the included angle for both triangles.
- Compare the two sides and the included angle.
- If both conditions are met, then the two triangles are congruent.
Examples
Practice Questions:
- Are triangles with sides \(10 \text{ cm}\), \(12 \text{ cm}\), and \(15 \text{ cm}\) and \(10 \text{ cm}\), \(12 \text{ cm}\), and \(14 \text{ cm}\) congruent by the SSS postulate?
- Are triangles with sides \(9 \text{ cm}\) and \(11 \text{ cm}\), and an included angle of \(45^{\circ}\), and another triangle with sides \(9 \text{ cm}\) and \(11 \text{ cm}\), with an included angle of \(45^{\circ}\) congruent by the SAS postulate?
- No
- Yes
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