Centroid and Centers of Triangles Flashcard

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

What is a median in a triangle?

Back

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

Front

If a median divides a triangle into two equal areas, what does this imply about the centroid?

Back

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

Front

What is the relationship between the lengths of segments created by the centroid on a median?

Back

If a median is divided by the centroid, the ratio of the lengths is 2:1.

Front

If AP = 12, what is AL? (AP is a segment of a median)

Back

AL = 18 (since the centroid divides the median in a 2:1 ratio).

Front

What is an angle bisector?

Back

An angle bisector is a line that divides an angle into two equal parts.

Front

What is a perpendicular bisector?

Back

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

Front

If LB = 4, what is CL? (LB is a segment of a median)

Back

CL = 4 (since CL is the midpoint of the opposite side).

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 NP = 5, what is CP? (NP is a segment of a median)

Back

CP = 10 (since the centroid divides the median in a 2:1 ratio).