Geometry Flashcard: Bisectors and Triangles

Front

What is a bisector in geometry?

Back

A bisector is a line, ray, or segment that divides an angle or a segment into two equal parts.

Front

What is the point of concurrency in a triangle?

Back

The point of concurrency is the point where three or more lines intersect. In triangles, common points of concurrency include the centroid, circumcenter, incenter, and orthocenter.

Front

Define circumcenter.

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 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 does it mean for a point to be equidistant from the sides of a triangle?

Back

It means that the distance from the point to each side of the triangle is the same.

Front

How do you find the circumradius of a triangle?

Back

The circumradius (R) can be found using the formula R = (abc)/(4K), where a, b, and c are the lengths of the sides of the triangle and K is the area of the triangle.

Front

What is the relationship between the incenter and the sides of a triangle?

Back

The incenter is the center of the circle inscribed in the triangle, and it is equidistant from all three sides.

Front

What is the formula for the area of a triangle using the inradius?

Back

The area (A) of a triangle can be calculated using the formula A = r * s, where r is the inradius and s is the semi-perimeter of the triangle.

Front

What is 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

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is also the center of mass of the triangle.