Grade 8 Theorems of Triangle Inequalities by Milo

The measure of the exterior angle is always greater than either of the two remote interior angles of a triangle.

• Theorem 1

• Theorem 2

• Theorem 3

• Theorem 4

The measure of an exterior angles is equal to the sum of the two remote interior angles.

• Theorem 1

• Theorem 2

• Theorem 3

• Theorem 4

The angle opposite the longest side is the largest angle.

• Theorem 1

• Theorem 2

• Theorem 3

The side opposite the largest angle is the longest side.

• Theorem 1

• Theorem 2

• Theorem 3

• Theorem 4

If side AB is the longest side, then what is the largest angle?

• ∠A

• ∠B

• ∠C

• ∠M

If ∠A is the smallest angle, then what is the shortest side?

• Side AB

• Side BC

• Side AC

• ∠M

If ∠C is the largest angle, then what is the longest side?

• Side AB

• Side BC

• Side AC

• ∠M

What theorem of triangle inequalities is not applicable in the picture?

• Theorem 1

• Theorem 3

• Theorem 4

• Theorem 5

Answer explanation

Theorem 1 (Exterior Angle Theorem) needs an exterior angle in order to be applicable.

m∠C < m∠A + m∠B. What theorem is observed from this given?

• Theorem 1

• Theorem 3

• Theorem 5

• Theorem 2

Answer explanation

The sum of any two sides of a triangle is always GREATER THAN the thirds side.

m∠W > m∠X. What theorem is observed from the given?

• Theorem 1

• Theorem 2

• Theorem 3

• Theorem 4

Answer explanation

Exterior Angle Inequality Theorem states that the measurement of an exterior angle is always GREATER THAN either of its two remote interior angles.