Unit 8 Retest

Front

What is the Centroid Theorem?

Back

The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side.

Front

If VT = 5, how long is VP if the centroid divides the median in a 2:1 ratio?

Back

VP = 10.

Front

In triangle ABC, if G is the centroid and BE = 18, what is the length of BG?

Back

BG = 12.

Front

What is the formula for the length of a midsegment in a triangle?

Back

The length of a midsegment is half the length of the third side.

Front

If the midsegment of a triangle is represented as 5x - 1, how do you find the value of x?

Back

Set the midsegment equal to half the length of the third side and solve for x.

Front

What type of line is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a right angle.

Front

What segments are drawn from the vertices to the centroid in a triangle?

Back

Medians.

Front

How do you calculate the length of a median in a triangle?

Back

Use the formula: Median = (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

What is the relationship between the centroid and the vertices of a triangle?

Back

The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

What is the significance of the centroid in triangle geometry?

Back

The centroid is the point where the three medians intersect and is the center of mass of the triangle.