Triangle Inequalities and Medians

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 two sides of a triangle are 8 and 12, what is the range of possible lengths for the third side?

Back

Front

How do you determine the longest side of a triangle given the side lengths?

Back

The longest side is the one with the greatest numerical value among the three side lengths.

Front

List the angles of a triangle in order from smallest to largest based on the side lengths 8, 12, and 15.

Back

The order is ∠A, ∠C, ∠B, where ∠A is opposite the shortest side (8), ∠C is opposite the medium side (12), and ∠B is opposite the longest side (15).

Front

Do the side lengths 2 inches, 2 inches, and 4 inches form a triangle?

Back

No, they do not form a triangle because 2 + 2 is not greater than 4.

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.

Front

How many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

Front

What is the relationship between the lengths of the medians and the sides of the triangle?

Back

The length of a median is always less than the length of the side it bisects.

Front

If the sides of a triangle are 5, 7, and 10, do they satisfy the Triangle Inequality Theorem?

Back

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

Front

What is the formula to find the length of a median in a triangle?

Back