Unique, more than one, or no triangle

Front

What is the Triangle Sum Theorem?

Back

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180°.

Front

What are the conditions for three lengths to form a triangle?

Back

The lengths must satisfy the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What is the definition of a unique triangle?

Back

A unique triangle is one that can be formed with a specific set of angle measures or side lengths, resulting in only one possible triangle.

Front

What does it mean if more than one triangle can be formed with given angle measures?

Back

It means that the angle measures allow for different configurations of triangles, typically seen in cases of ambiguous cases in the Law of Sines.

Front

What is an ambiguous case in triangle problems?

Back

An ambiguous case occurs when two sides and a non-included angle (SSA) are known, leading to the possibility of zero, one, or two triangles.

Front

How do you find a missing angle in a triangle?

Back

To find a missing angle, subtract the sum of the known angles from 180°.

Front

What is the relationship between the angles and sides of a triangle?

Back

In a triangle, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

What is the significance of the angle measures 55°, 45°, and 90°?

Back

These angle measures do not form a triangle because they do not sum to 180°.

Front

What is the definition of a triangle?

Back

A triangle is a polygon with three edges and three vertices.

Front

What is the Law of Sines?

Back

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides and angles.