Medians and Altitudes

Front

What is a median of a triangle?

Back

A segment with endpoints at the vertex and midpoint of the opposite side.

Front

What is an altitude of a triangle?

Back

A segment that connects a vertex to the opposite side at a right angle.

Front

What is the point of concurrency of the medians of a triangle called?

Back

Centroid.

Front

What is the point of concurrency of the altitudes of a triangle called?

Back

Orthocenter.

Front

What is the circumcenter of a triangle?

Back

The point where the perpendicular bisectors of the sides intersect.

Front

How do you find the length of a median in 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 adjacent to the median, and c is the length of the opposite side.

Front

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

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Front

Can a segment be both a median and an altitude?

Back

Yes, in an isosceles triangle, the segment from the vertex angle to the base can be both a median and an altitude.

Front

What is the formula to find the area of a triangle using the base and height?

Back

Area = 1/2 * base * height.

Front

What is the significance of the circumcenter in triangle construction?

Back

The circumcenter is the center of the circumcircle, which passes through all three vertices of the triangle.