Median and Altitude

Front

What is the definition of 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 definition of an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

If X is the centroid of a triangle and ZX = 3, what is AZ?

Back

AZ = 9.

Front

If X is the centroid of a triangle and BX = 8, what is BY?

Back

BY = 12.

Front

Is segment AB a median, altitude, neither or both if it connects a vertex to the midpoint of the opposite side?

Back

AB is a median.

Front

Is segment AB a median, altitude, neither or both if it is perpendicular to the opposite side?

Back

AB is an altitude.

Front

What is the relationship between the centroid and the segments connecting it to 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.

Front

If CW = 30 and X is the centroid, what is CX?

Back

CX = 20.

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.

Front

What is the formula to find the length of an altitude in a triangle?

Back

The length of an altitude can be calculated using the formula: h = (2 * Area) / base.