Triangle Properties and Centers of Triangles Review

Front

What is the definition of an orthocenter in a triangle?

Back

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

Front

What is a perpendicular bisector in a triangle?

Back

A perpendicular bisector is a line that divides a side of the triangle into two equal parts at a right angle.

Front

How do you find the circumcenter of a triangle?

Back

The circumcenter can be found by constructing the perpendicular bisectors of at least two sides of the triangle; the point where they intersect is the circumcenter.

Front

What is the relationship between the lengths of segments created by a median in a triangle?

Back

A median divides a triangle into two segments, where the segment connecting the vertex to the centroid is twice as long as the segment connecting the centroid to 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, and it is also the center of mass of the triangle.

Front

If GC is 11, what is AG if G is the midpoint of AC?

Back

AG is also 11, since G is the midpoint.

Front

What is the formula for finding the length of a median in a triangle?

Back

The length of a median can be calculated using the formula: m = 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 side opposite the median.

Front

What is the significance of the circumradius in a triangle?

Back

The circumradius is the radius of the circumcircle, which is the circle that passes through all three vertices of the triangle.

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 a median in a triangle?

Back

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