GEOM Inequalities in Triangles

Front

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

Back

Yes, these lengths satisfy the triangle inequality theorem.

Front

Order the sides from greatest to least: 5, 7, 10

Back

10, 7, 5

Front

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

Back

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

Front

Two sides of a triangle have side lengths of 17 meters and 12 meters. What is the range of possible lengths for the third side?

Back

5 < x < 29

Front

Do the side lengths of 4, 4, 4 form a triangle?

Back

True, they form an equilateral triangle.

Front

What is the triangle inequality theorem?

Back

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If one side of a triangle is 8 and the other is 5, what is the maximum length of the third side?

Back

The maximum length is 12 (8 + 5 - 1).

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 minimum length of the third side if two sides are 6 and 10?

Back

The minimum length is 5 (10 - 6 + 1).

Front

Can a triangle have sides of lengths 2, 2, and 5?

Back

No, these lengths do not satisfy the triangle inequality theorem.