key term - SSS Triangle

Definition

The SSS triangle, or Side-Side-Side triangle, is a type of triangle where all three sides are known. This is one of the fundamental ways to determine the unique properties of a triangle, including its angles and area, without any additional information.

5 Must Know Facts For Your Next Test

1. The SSS triangle is one of the three ways to determine the congruence of two triangles, along with the ASA (Angle-Side-Angle) and AAS (Angle-Angle-Side) methods.
2. The Law of Cosines can be used to find the third side of an SSS triangle when the lengths of the other two sides and the angle between them are known.
3. Heron's Formula can be used to calculate the area of an SSS triangle when the lengths of all three sides are known.
4. The SSS triangle is a fundamental building block for many geometric proofs and constructions.
5. The unique properties of an SSS triangle, such as its angles and area, can be used to solve a variety of real-world problems in fields like engineering, architecture, and navigation.

Review Questions

• Explain how the SSS triangle is used to determine the congruence of two triangles.
  • The SSS (Side-Side-Side) triangle is one of the three fundamental ways to establish the congruence of two triangles. If the corresponding sides of two triangles are equal in length, then the triangles are congruent. This means they have the same size and shape, with all their corresponding angles and sides being equal. The SSS criterion is a powerful tool for proving the congruence of triangles without needing to know their angles.
• Describe how the Law of Cosines can be applied to an SSS triangle.
  • The Law of Cosines is a formula that can be used to find the third side of a triangle when the lengths of the other two sides and the angle between them are known. In the case of an SSS triangle, where all three sides are given, the Law of Cosines can be used to determine the angle between any two of the sides. This relationship between the side lengths and the angle allows for the calculation of the third angle, which, along with the side lengths, fully defines the properties of the SSS triangle.
• Analyze how Heron's Formula can be used to calculate the area of an SSS triangle.
  • Heron's Formula provides a way to calculate the area of a triangle given the lengths of all three sides, without needing to know the angles. This is particularly useful for the SSS triangle, where the side lengths are the only information provided. By plugging the three side lengths into Heron's Formula, you can determine the exact area of the SSS triangle. This formula is a valuable tool for solving problems in fields like engineering and construction, where the dimensions of a triangle are known, but the angles may not be.

Related terms

Congruent Triangles: Congruent triangles are triangles that have the same size and shape, meaning all their corresponding sides and angles are equal.

Law of Cosines:

The Law of Cosines is a formula used to find the third side of a triangle given the lengths of the other two sides and the angle between them.

Heron's Formula:

Heron's Formula is a way to calculate the area of a triangle given the lengths of all three sides, without needing to know the angles.