Medians, altitudes, angle bisectors, and perpendicular bisectors

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 relationship between the lengths of segments created by an angle bisector in a triangle?

Back

The angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides.

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 identify a perpendicular bisector in a triangle?

Back

A perpendicular bisector can be identified as the line segment that is perpendicular to a side of the triangle and passes through its midpoint.

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

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

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 median, 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 find 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 the relationship between the angle bisector and the opposite side of a triangle?

Back

The angle bisector theorem states that the angle bisector divides the opposite side into segments that are proportional to the adjacent sides.