6.3 Medians and Altitudes

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.

Tags

CCSS.HSG.CO.C.10

Front

What are medians in a triangle?

Back

Medians are line segments that connect a vertex of the triangle to the midpoint of the opposite side.

Tags

CCSS.HSG.CO.C.10

Front

How do you find the length of AG if AD = 12 in a triangle where G is the centroid?

Back

Since G divides the median in a 2:1 ratio, AG = 8.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

The centroid is the point of concurrency of the three medians of a triangle.

Tags

CCSS.HSG.CO.C.10

Front

If TP = 27, what is ZP if G is the centroid?

Back

ZP = 9, since the centroid divides the median in a 2:1 ratio.

Tags

CCSS.HSG.CO.C.10

Front

What is the orthocenter of a triangle?

Back

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

Tags

CCSS.HSG.CO.C.10

Front

What are altitudes in a triangle?

Back

Altitudes are perpendicular segments from a vertex to the line containing the opposite side.

Front

How do you find the length of ZQ if Z is a vertex and Q is the foot of the altitude from Z?

Back

If ZQ is given as 4, then it is the length of the altitude from vertex Z to side XY.

Front

What is the difference between a median and an altitude in a triangle?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude is perpendicular to the opposite side.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the balance point of the triangle and divides each median into a 2:1 ratio.

Tags

CCSS.HSG.CO.C.10