Unit 5 Test

Front

What is a centroid in a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is also the center of mass of the triangle.

Front

How do you find the measure of a side in a triangle when given the centroid?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Front

What is the Triangle Inequality Theorem?

Back

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

Given two sides of a triangle measuring 12 and 7, what is the range of possible lengths for the third side?

Back

5 < x < 19.

Front

True or False: A triangle can have side lengths of 8, 9, and 15.

Back

True.

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 FG = HG and m

Back

Use the property of angles in a triangle and the fact that FG = HG to set up an equation and solve for m

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side.

Front

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

Back

Use the Triangle Inequality Theorem: check if the sum of any two sides is greater than the third side.

Front

What is the significance of the centroid in triangle geometry?

Back

The centroid is the balance point of the triangle and is important in various applications, including physics and engineering.