5.4 Inequalities in One Triangle

Front

What is the Triangle Inequality Theorem?

Back

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

Front

How do you determine the longest side of a triangle?

Back

The longest side of a triangle is opposite the largest angle. To find it, first identify the angles and order them from largest to smallest.

Front

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

Back

In a triangle, the larger the angle, the longer the side opposite that angle.

Front

If two angles of a triangle are known, how can you find the third angle?

Back

The third angle can be found by subtracting the sum of the known angles from 180 degrees.

Front

What does it mean for a triangle to be constructed with given side lengths?

Back

A triangle can be constructed with given side lengths if they satisfy the Triangle Inequality Theorem.

Front

How do you order the sides of a triangle based on the angles?

Back

Order the sides from longest to shortest based on the corresponding angles from largest to smallest.

Front

What is the significance of the longest side in a triangle?

Back

The longest side is crucial for determining the triangle's properties and can help in solving for angles and other sides.

Front

Can a triangle be formed with sides of lengths 5, 10, and 15?

Back

No, because 5 + 10 is not greater than 15, violating the Triangle Inequality Theorem.

Front

What is the formula to find the area of a triangle?

Back

Area = 1/2 * base * height.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.