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.

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

Orthocenter.

Tags

CCSS.HSG.CO.C.10

Front

What is the circumcenter of a triangle?

Back

The point where the perpendicular bisectors of the sides intersect.

Tags

CCSS.HSG.C.A.3

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.

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

Area = 1/2 * base * height.

Tags

CCSS.6.G.A.1

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.

Tags

CCSS.HSG.C.A.3