Special Segments in Triangles

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect. It is also the center of the circle inscribed within the triangle.

Front

What is an angle bisector?

Back

An angle bisector is a ray that divides an angle into two congruent angles.

Front

What is a median in a triangle?

Back

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

Front

What is an altitude in a triangle?

Back

An altitude is a segment from a vertex of the triangle that is perpendicular to the line containing the opposite side.

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

How do you find the incenter of a triangle?

Back

To find the incenter, construct the angle bisectors of each angle of the triangle. The point where they intersect is the incenter.

Front

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

Back

The incenter is equidistant from all three sides of the triangle.

Front

What is the significance of the centroid in 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

How do you calculate 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 opposite side.

Front

What is the difference between a median and an altitude?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude connects a vertex to the opposite side at a right angle.