5.5 Medians and Altitudes

Front

What is the definition of an altitude in a triangle?

Back

An altitude is a segment joining a vertex to the opposite side so that it is perpendicular to that side.

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.

Front

If G is the centroid of triangle ABC and AC = 32, what is the length of segment CE?

Back

The length of segment CE is 16.

Front

What type of lines are the altitudes in a triangle?

Back

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

Front

How do you find the orthocenter of a triangle?

Back

The orthocenter is found by determining the intersection point of the altitudes of the triangle.

Front

What is the definition of a median in a triangle?

Back

A median is a segment joining a vertex to the midpoint of the opposite side.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the center of mass and divides each median into a ratio of 2:1.

Front

How many medians does a triangle have?

Back

A triangle has three medians.

Front

What is the formula to find the coordinates of the centroid of a triangle with vertices (x1, y1), (x2, y2), (x3, y3)?

Back

The coordinates of the centroid (G) are given by G = ((x1+x2+x3)/3, (y1+y2+y3)/3).

Front

What is the relationship between the orthocenter and the altitudes of a triangle?

Back

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