Triangle Inequality Theorem

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 sides of a triangle are 3 cm, 4 cm, and 5 cm, do they satisfy the Triangle Inequality Theorem?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

Can the side lengths 2 cm, 2 cm, and 5 cm form a triangle?

Back

No, because 2 + 2 is not greater than 5.

Front

What is the minimum length of the third side if two sides of a triangle are 7 cm and 10 cm?

Back

The minimum length of the third side must be greater than 3 cm (10 - 7).

Front

What is the maximum length of the third side if two sides of a triangle are 7 cm and 10 cm?

Back

The maximum length of the third side must be less than 17 cm (7 + 10).

Front

If a triangle has sides of lengths 8 cm, 15 cm, and x cm, what is the range of possible values for x?

Back

x must be greater than 7 cm and less than 23 cm.

Front

What is the relationship between the angles and sides 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

If two angles of a triangle are 30 degrees and 60 degrees, what is the measure of the third angle?

Back

The third angle is 90 degrees, because the sum of angles in a triangle is 180 degrees.

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.