5.1-5.3 Review

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is located two-thirds of the distance from each vertex to the midpoint of the opposite side.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices of the triangle.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the three altitudes of a triangle intersect. Its position can be inside, on, or outside the triangle depending on the type of triangle.

Front

Define a median in a triangle.

Back

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

Front

Define an altitude in a triangle.

Back

An altitude is a perpendicular segment from a vertex to the line containing 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 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

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle. The point where they intersect is the circumcenter.

Front

What is the significance of the incenter in triangle construction?

Back

The incenter is the center of the inscribed circle (incircle) of the triangle, which is tangent to all three sides.

Front

What is the special property of the circumcenter?

Back

The circumcenter is equidistant from all three vertices of the triangle.