Centroid and Midsegment

Front

What is the centroid of 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 length of a midsegment in a triangle?

Back

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

Front

If G is the centroid of triangle ABC, what is the ratio of the lengths of the segments created by the centroid on each median?

Back

The ratio is 2:1, with the longer segment being closer to the vertex.

Front

What is a midsegment in a triangle?

Back

A midsegment is a segment that connects the midpoints of two sides of a triangle.

Front

If BE = 18 and G is the centroid, what is the length of BG?

Back

BG = 12, since G divides the median in a 2:1 ratio.

Front

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

Back

BE = 21, since G divides the median in a 2:1 ratio.

Front

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

Back

Midsegments are parallel to one side of the triangle and half its length.

Front

How can you determine if two segments are parallel in a triangle?

Back

If they are both midsegments, they are parallel to the third side of the triangle.

Front

What is the formula for finding the area of a triangle using the centroid?

Back

Area = 1/3 * base * height, where the base is the length of one side and height is the perpendicular distance from the opposite vertex.

Front

What is the significance of the centroid in real-world applications?

Back

The centroid can represent the center of mass in physical objects, which is important in engineering and design.