Triangle Inequalities Practice (includes 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 2.5 and 7.25, what is the range of possible lengths for the third side?

Back

4.75 < x < 9.75

Front

Which of the following lengths cannot represent the sides of a triangle: 32, 34, 60, 28, 30, 58, 13, 20, 27, 2, 4, 5?

Back

28, 30, 58

Front

What is a median in a triangle?

Back

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

Front

If G is the centroid of triangle ABC and GE = 7, what is the length of BE?

Back

21

Front

How do you determine if three lengths can form a triangle?

Back

Check if the sum of the lengths of any two sides is greater than the length of the third side.

Front

Order the sides from least to greatest: BC, AC, AB.

Back

BC, AC, AB

Front

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

Back

The length of a median can be calculated using the formula: m = 1/2 * sqrt(2a^2 + 2b^2 - c^2), where a and b are the lengths of the sides adjacent to the median, and c is the length of the opposite side.

Front

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

Back

7 < x < 17

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the point where the three medians intersect, and it divides each median into a ratio of 2:1.