Medians, altitudes, angle bisectors, and perpendicular bisectors

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

How do you find the length of a median in a triangle?

Back

To find the length of a median, use 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 vertex, and c is the length of the opposite side.

Front

What is an altitude in a triangle?

Back

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

Front

How do you calculate the area of a triangle using an altitude?

Back

The area of a triangle can be calculated using the formula: Area = (1/2) * base * height, where the height is the length of the altitude.

Front

What is an angle bisector?

Back

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

Front

What is the Angle Bisector Theorem?

Back

The Angle Bisector Theorem states that the ratio of the lengths of the two segments created by the angle bisector on the opposite side is equal to the ratio of the lengths of the other two sides of the triangle.

Front

What is a perpendicular bisector?

Back

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

Front

How do you find the equation of a perpendicular bisector?

Back

To find the equation of a perpendicular bisector, first find the midpoint of the segment, then determine the slope of the segment, and use the negative reciprocal of that slope for the perpendicular line.

Front

What is the relationship between medians and centroids in a triangle?

Back

The centroid of a triangle is the point where all three medians intersect, and it divides each median into a ratio of 2:1.

Front

What is the significance of the circumcenter in relation to perpendicular bisectors?

Back

The circumcenter is the point where the perpendicular bisectors of a triangle intersect, and it is equidistant from all three vertices of the triangle.