Triangle Inequalities

Triangle Inequality #1 Triangle Inequality 1(577031).ggb

A side of a triangle is always greater than the difference (subtraction) of the other two sides

AND smaller than their sum (addition).

Example:

This same relation applies to sides b and c.

Example (I Do)Can there be a triangle with sides 3cm, 4cm and 5cm long?

Example (We Do)If one side of a triangle measures 3cm and another side measures 7cm, what are the possible lengths of the third side?

Example (You Do)Can there be a triangle with sides 2cm, 3cm and 5cm long?

Triangle Inequality #2In a triangle: the smallest side is opposite to the smallest angle the medium side is opposite to the medium angle the biggest side is opposite to the biggest angle.

For example:

Geogebra Demonstration (largest side opposite to largest angle...)

Example ( I Do)

Order the sides from largest to smallest.

Example (We Do)

Order the angles from smallest to largest.

Example (You Do)

Which is the largest side?Which is the smallest side?

Triangle Inequality #3 (Hinge Theorem)

If two sides of a triangle are equal to two sides of another triangle but the angle included between those two sides are not equal, then the triangle with the smallest included angle has the smallest third side

Example (I Do)

Example (We Do)Use the hinge theorem to find the possible values of x.

Example (You Do)