Triangle Inequality Theorem

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 a triangle has sides of lengths a, b, and c, what must be true?

Back

a + b > c, a + c > b, and b + c > a.

Front

Identify the shortest side in a triangle with sides 3, 4, and 5.

Back

The shortest side is 3.

Front

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

Back

The largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

If one side of a triangle is 7 and another is 10, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 3 and less than 17.

Front

What is the smallest angle in a triangle with angles 30°, 60°, and 90°?

Back

The smallest angle is 30°.

Front

In triangle ABC, if side AB = 8 and side AC = 6, what is the maximum possible length of side BC?

Back

The maximum possible length of side BC is less than 14.

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 largest angle in a triangle with angles 45°, 45°, and 90°?

Back

The largest angle is 90°.

Front

If a triangle has sides of lengths 5, 12, and x, what is the range of values for x?

Back

x must be greater than 7 and less than 17.