Discovering the Magic of SSS and SAS Congruence in Triangles

SSS proves two triangles congruent when all three pairs of sides match. SAS proves it when two pairs of sides and the angle between them match, and the angle must be the included one for the proof to hold.

• 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.

Worked examples: SSS and SAS congruence

Practice questions on SSS and SAS congruence

1. 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?
2. 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?

1. No
2. Yes

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