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

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

What is an angle bisector?

Back

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

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 length of a median in a triangle?

Back

The length of a median can be found 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 vertex and c is the length of the opposite side.

Front

What is the relationship between the lengths of the sides of a triangle and its medians?

Back

The lengths of the medians are related to the lengths of the sides of the triangle, and they can be calculated using specific formulas.

Front

What is the significance of the centroid in relation to medians?

Back

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

Front

How do you determine if a line segment is a perpendicular bisector?

Back

A line segment is a perpendicular bisector if it is perpendicular to another segment and divides it into two equal parts.

Front

What is the relationship between angle bisectors and triangle areas?

Back

The angle bisector of a triangle divides it into two smaller triangles with equal areas.

Front

How can you identify a perpendicular bisector in a coordinate plane?

Back

A perpendicular bisector can be identified by finding the midpoint of a segment and determining the slope that is negative reciprocal to the original segment's slope.