Types of Triangles

The interior angles of every triangle always add up to 180°.

1. Add the measures of the two known angles.
2. Subtract their sum from 180°.
3. The remaining value is the third angle of the triangle.

Formula: third angle = 180° − first angle − second angle.

The interior angles of every triangle always add up to 180°.

1. Add the measures of the two known angles.
2. Subtract their sum from 180°.
3. The remaining value is the third angle of the triangle.

Formula: third angle = 180° − first angle − second angle.

For three segments to form a triangle, the third side must be shorter than the sum of the two given sides and longer than their difference.

1. Add the given side lengths: {a} + {b}. The third side must be shorter than this sum.
2. Find the difference between the given side lengths: |{a} − {b}|. The third side must be longer than this difference.
3. Choose the listed length that satisfies both conditions.

Rule: if the third side has length c, then |{a} − {b}| < c < {a} + {b}.

A triangle is classified by its greatest angle.

• If one angle is exactly 90°, the triangle is right-angled.
• If one angle is greater than 90°, the triangle is obtuse-angled.
• If all three angles are less than 90°, the triangle is acute-angled.

Find the greatest given angle and use these conditions to select the triangle type.

A triangle is classified by comparing the lengths of all three sides.

• If all three sides are equal, the triangle is equilateral.
• If exactly two sides are equal, the triangle is isosceles.
• If all three side lengths are different, the triangle is scalene.

Compare the three given lengths and select the matching type.