Inequalities in Triangles

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 the lengths of two sides of a triangle are 10 inches and 17 inches, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than |10 - 17| = 7 inches and less than 10 + 17 = 27 inches. So, it must be between 7 and 27 inches.

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.

Front

How can you determine the longest side of a triangle given its angles?

Back

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

Front

What is an obtuse triangle?

Back

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

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle equal to 90 degrees.

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 sum of the interior angles of a triangle?

Back

The sum of the interior angles of a triangle is always 180 degrees.

Front

Can a triangle have two obtuse angles?

Back

No, a triangle cannot have two obtuse angles because the sum of the angles would exceed 180 degrees.