Triangle Inequalities

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

If a triangle has sides of lengths 7, 10, and x, what is the range of possible values for x?

Back

x must be greater than 3 and less than 17 (3 < x < 17).

Front

What is an angle bisector?

Back

An angle bisector is a line or ray that divides an angle into two equal parts.

Front

How do you determine the largest angle in a triangle?

Back

The largest angle in a triangle is opposite the longest side.

Front

Can a triangle have sides of lengths 5, 10, and 15?

Back

No, because 5 + 10 is not greater than 15.

Front

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

Back

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

Front

If two sides of a triangle are equal, what type of triangle is it?

Back

It is an isosceles triangle.

Front

What is the range of possible lengths for the third side of a triangle with sides 8 and 6?

Back

The third side must be greater than 2 and less than 14 (2 < x < 14).

Front

What is the sum of the angles in any triangle?

Back

The sum of the angles in any triangle is always 180 degrees.

Front

If a triangle has angles of 30° and 60°, what is the measure of the third angle?

Back

The third angle measures 90° (180° - 30° - 60°).