Triangle Special Segments

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 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 a perpendicular bisector?

Back

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

Front

What is an altitude in a triangle?

Back

An altitude is a line segment from a vertex to the opposite side, forming a right angle with that side.

Front

How many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

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 2:1 ratio.

Front

What is the significance of the centroid in a triangle?

Back

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

Front

What is the difference between an altitude and a median?

Back

An altitude is perpendicular to the opposite side, while a median connects a vertex to the midpoint of the opposite side.

Front

Can a segment be both a median and an altitude?

Back

Yes, in an isosceles triangle, the median from the vertex angle to the base is also an altitude.

Front

What is the formula for finding the length of a median in a triangle?

Back

The length of a median can be calculated 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 side opposite the median.