Medians of Triangles (Practice)

Front

What is a median in a triangle?

Back

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

Front

What is the centroid of a triangle?

Back

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

Tags

CCSS.HSG.CO.C.10

Front

If AG is 16, what is GD if G is the centroid?

Back

GD is 8, since the centroid divides each median in a 2:1 ratio.

Tags

CCSS.HSG.CO.C.10

Front

If AD = 12, what is AG?

Back

AG is 8, as the centroid divides the median in a 2:1 ratio.

Tags

CCSS.HSG.CO.C.10

Front

What is the ratio in which the centroid divides the median?

Back

The centroid divides each median in a 2:1 ratio.

Tags

CCSS.HSG.CO.C.10

Front

Which point in a triangle is known as the orthocenter?

Back

The orthocenter is the point where the three altitudes of a triangle intersect.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

The length from the vertex to the centroid is twice the length from the centroid to the midpoint of the opposite side.

Tags

CCSS.HSG.CO.C.10

Front

If NP = 5, what is CP?

Back

CP is 10, as the centroid divides the median in a 2:1 ratio.

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.HSG.CO.C.10

Front

What is the significance of the centroid in a triangle?

Back

The centroid is significant because it is the balance point of the triangle and divides each median into two segments with a 2:1 ratio.

Tags

CCSS.HSG.CO.C.10