Inequalities in Triangles

Front

Can the sides of a triangle have lengths 3, 8, and 9?

Back

Yes, the triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.

Front

Name the largest angle in a triangle with sides 5, 7, and 9.

Back

The largest angle is opposite the longest side, which is 9.

Front

If the given side lengths of a triangle are 16 and 10, what can be the third side?

Back

The third side must be less than 26 and greater than 6, so possible lengths include 25, 22, 21, etc.

Front

What is a possible third side to a triangle with side lengths of 5 and 5?

Back

The third side must be less than 10 and greater than 0, so a possible length is 9.

Front

Find the value of x using the exterior angle theorem: If ∠A + ∠B = ∠C, what is ∠C?

Back

∠C is equal to the sum of the two opposite interior angles.

Front

What is the triangle inequality theorem?

Back

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If one angle of a triangle is 90 degrees, what type of triangle is it?

Back

It is a right triangle.

Front

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

Back

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

How do you determine if three lengths can form a triangle?

Back

Use the triangle inequality theorem: check if the sum of the lengths of any two sides is greater than the length of the third side.

Front

What is an exterior angle of a triangle?

Back

An exterior angle is formed by one side of the triangle and the extension of an adjacent side.