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: For education statistics and research, visit the National Center for Education Statistics.

• 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: For education statistics and research, visit the National Center for Education Statistics.

• 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? For education statistics and research, visit the National Center for Education Statistics.

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. For education statistics and research, visit the National Center for Education Statistics.

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? For education statistics and research, visit the National Center for Education Statistics.

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. For education statistics and research, visit the National Center for Education Statistics.

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: For education statistics and research, visit the National Center for Education Statistics.

1. No
2. Yes