Discovering the Magic of SSS and SAS Congruence in Triangles

Step-by-step Guide: SSS and SAS Congruence

1. SSS (Side-Side-Side) Congruence Postulate:
If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. To use this postulate:

• 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.

2. SAS (Side-Angle-Side) 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. To use this postulate:

• 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

Example 1:
Are triangles with sides \(4 \text{ cm}\), \(5 \text{ cm}\), and \(6 \text{ cm}\) and \(4 \text{ cm}\), \(5 \text{ cm}\), and \(6 \text{ cm}\) congruent based on the SSS postulate?

Solution:
Both triangles have sides of:
\(4 \text{ cm}, 5 \text{ cm}, \text{ and } 6 \text{ cm}\)
Since the sides match exactly, the two triangles are congruent by the SSS postulate.

Example 2:
Are triangles with sides \(7 \text{ cm}\) and \(8 \text{ cm}\), and an included angle of \(60^{\circ}\), and another triangle with sides \(7 \text{ cm}\) and \(8 \text{ cm}\), with an included angle of \(60^{\circ}\) congruent based on the SAS postulate?

Solution:
Both triangles have:
Sides of \(7 \text{ cm} \text{ and } 8 \text{ cm}\)
An included angle of \(60^{\circ}\)
Since both the sides and the included angles match, the two triangles are congruent by the SAS postulate.

Practice Questions:

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?

Answers:

1. No
2. Yes