Triangle inequality

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 a triangle has sides of lengths 5, 7, and 10, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 5 + 7 > 10, 5 + 10 > 7, and 7 + 10 > 5.

Front

What type of triangle has all sides of different lengths?

Back

Scalene triangle.

Front

What type of triangle has at least two sides of equal length?

Back

Isosceles triangle.

Front

What type of triangle has all sides of equal length?

Back

Equilateral triangle.

Front

Can a triangle have side lengths of 2, 3, and 6?

Back

No, because 2 + 3 is not greater than 6.

Front

What is the maximum length of the third side of a triangle with sides of lengths 8 and 6?

Back

The maximum length is less than 14 (8 + 6).

Front

What is the minimum length of the third side of a triangle with sides of lengths 8 and 6?

Back

The minimum length is greater than 2 (8 - 6).

Front

If a triangle has sides of lengths 7, 24, and 25, what type of triangle is it?

Back

It is a right triangle, as 7² + 24² = 25².

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.