Medians and Centroid and Altitudes and Orthocenter

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

If a triangle has sides of length 11 and 11, what is the length of the median to the base?

Back

The length of the median to the base is equal to the length of the base, which is 11.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and it divides each median into a ratio of 2:1.

Front

How do you find the length of a median given two sides of a triangle?

Back

Use the formula: Median = 1/2 * sqrt(2a^2 + 2b^2 - c^2), where a and b are the lengths of the sides and c is the length of the base.

Front

What is an altitude in a triangle?

Back

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

Front

What is the orthocenter of a triangle?

Back

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

Front

If G is the centroid and GE = 7, what is the length of BE?

Back

The length of BE is 21.

Front

If G is the centroid and GF = 4, what is the length of GC?

Back

The length of GC is 8.

Front

In triangle ABC, if AD is a median and DC = 11, what is the length of AD?

Back

The length of AD is 11.

Front

In triangle XYZ, if YC = 15 and YB, XC, and ZA are medians, what is the length of YZ?

Back

The length of YZ is 30.