Centers of Triangles Review

Front

What is the definition of an angle bisector in a triangle?

Back

An angle bisector is a line segment that divides an angle into two equal parts.

Front

What is the orthocenter of a triangle?

Back

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

Front

What segments intersect at the centroid of a triangle?

Back

The centroid is the intersection of the three medians of a triangle.

Front

How do you find the length of a segment from the centroid to a vertex?

Back

The length from the centroid to a vertex is two-thirds the length of the median from that vertex.

Front

What is the definition of a centroid in a triangle?

Back

The centroid is the point where the three medians of a triangle intersect.

Front

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

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 of the opposite side.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the three angle bisectors of a triangle intersect.

Front

What is the significance of the incenter in a triangle?

Back

The incenter is the center of the circle inscribed within the triangle (incircle).

Front

What is the relationship between angle bisectors and the sides of a triangle?

Back

The angle bisector of a triangle divides the opposite side into segments that are proportional to the lengths of the other two sides.

Front

How do you find the length of segments created by angle bisectors?

Back

If an angle bisector divides the opposite side into segments of lengths a and b, then a/b = c/d, where c and d are the lengths of the other two sides.