Wed 11/15 CW Center of triangles

Front

What is the point of concurrency where the three medians of a triangle intersect?

Back

centroid

Front

In triangle geometry, what is the term for the point where the perpendicular bisectors of the sides intersect?

Back

circumcenter

Front

What is the relationship between the centroid and the segments it creates on the medians of a triangle?

Back

The centroid divides each median into two segments, with the segment connecting the vertex to the centroid being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

If the centroid of triangle RST is V, and SV = 6, what is the length of the segment connecting the vertex S to the midpoint of side RT?

Back

9

Front

What is the definition of a median in a triangle?

Back

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

Front

How do you find the length of a segment in a triangle when given the lengths of other segments and the centroid?

Back

Use the properties of the centroid, which divides the median in a 2:1 ratio.

Front

What is the significance of the circumcenter in triangle geometry?

Back

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

Front

What is the formula to find the length of a median in a triangle given the lengths of the sides?

Back

The length of a median can be calculated using the formula: m_a = (1/2) * sqrt(2b^2 + 2c^2 - a^2), where m_a is the median to side a, and b and c are the other two sides.

Front

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

Back

The centroid divides the triangle into three smaller triangles of equal area.

Front

What is the definition of the orthocenter in a triangle?

Back

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