Medians and Altitudes (5.4)

Front

What is a median of a triangle?

Back

A median of a triangle is a segment with endpoints at a vertex and 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.

Front

What is an altitude of a triangle?

Back

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

Front

Where do the altitudes of a triangle intersect?

Back

The altitudes of a triangle intersect at the orthocenter.

Front

If a median divides a triangle into two equal areas, what does this imply?

Back

It implies that the median connects a vertex to the midpoint of the opposite side.

Front

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

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

How do you find the length of a median in a triangle?

Back

You can use the formula: Median = 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 difference between a median and a midsegment in a triangle?

Back

A median connects a vertex to the midpoint of the opposite side, while a midsegment connects the midpoints of two sides of the triangle.

Front

If BF = 10 in triangle ABC and CF is a median, what is AF?

Back

AF = 10, since the median divides the opposite side into two equal segments.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect.