Inequalities in Triangles An inequality in a triangle relates the lengths of its sides or angles. These inequalities can tell us whether one side is long...
An inequality in a triangle relates the lengths of its sides or angles. These inequalities can tell us whether one side is longer than another, or whether one angle is greater than another.
Examples:
If two sides of a triangle have lengths 5 cm and 7 cm, then the third side must be at least 3 cm long.
If the angles in a triangle add up to 180°, then the angles must be equal.
If one angle in a triangle is obtuse (greater than 90°), then the other two angles must be acute (less than 90°).
Why are inequalities important?
Inequalities can be used to solve problems about triangles, such as finding the length of a missing side or angle, or determining if two triangles are similar.
Here are some important inequalities in triangles:
Side-Side-Side: The longest side is always greater than the other two sides.
Angle-Angle-Side: The angles opposite the larger angles are greater than the angles opposite the smaller angles.
Sum of angles in a triangle is always 180°: This means that the angles in a triangle will always add up to 180°.
Remember:
An inequality can be true for some triangles and false for others.
The order of the sides or angles in an inequality does not matter.
An inequality can be used to prove other theorems about triangles