4.2 review

Front

The point of concurrency of the 3 medians of a triangle is called the ___?

Back

Centroid

Front

What is the definition of a median in a triangle?

Back

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

Front

What is the difference between the centroid and the circumcenter of a triangle?

Back

The centroid is the point where the three medians intersect, while the circumcenter is the point where the perpendicular bisectors of the sides intersect.

Front

How many medians does a triangle have?

Back

A triangle has three medians.

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 circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of the triangle intersect.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is the center of the triangle's incircle.

Front

What is the formula for finding the centroid of a triangle given its vertices (x1, y1), (x2, y2), (x3, y3)?

Back

The centroid (G) can be found using the formula G = ((x1+x2+x3)/3, (y1+y2+y3)/3).

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the center of mass of the triangle and is the balance point.

Front

What is a midsegment in a triangle?

Back

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