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, you can 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 line segment from a vertex to the line containing the opposite side.

Front

How do you determine the length of an altitude in a triangle?

Back

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

Front

What is an angle bisector?

Back

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

Front

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

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 can 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 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 find the centroid of a triangle given its vertices?

Back

The centroid (G) can be found using the formula: G = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3), where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices.