Special Segments in Triangles

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 segment from a vertex to the line containing the opposite side.

Front

What is a midsegment in a triangle?

Back

A midsegment is a segment that connects the midpoints of two sides of a triangle.

Front

What is an angle bisector in a triangle?

Back

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

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 length of a median in a triangle?

Back

The length of a median can be found using the formula: m = 1/2 * √(2a² + 2b² - c²), 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 relationship between the medians of a triangle?

Back

The three medians of a triangle intersect at a point called the centroid, which divides each median into a ratio of 2:1.

Front

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

Back

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

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the point where the three medians intersect and is the center of mass of the triangle.

Front

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

Back

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