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 a perpendicular bisector?

Back

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

Front

What is an angle bisector?

Back

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

Front

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

Back

Use the formula: Median = 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 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 determine if a segment is a perpendicular bisector?

Back

A segment is a perpendicular bisector if it is perpendicular to the segment it bisects and divides it into two equal lengths.

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

How do you find the area of a triangle using the altitude?

Back

Area = 1/2 * base * height, where height is the length of the altitude.