Special Segments in Triangles

Front

What is a special segment in a triangle?

Back

A special segment in a triangle refers to segments such as medians, angle bisectors, altitudes, and perpendicular bisectors that have specific properties and functions within the triangle.

Front

Define a median of a triangle.

Back

A median of a triangle is a segment that connects a vertex to the midpoint of the opposite side.

Front

What is an angle bisector?

Back

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

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a segment that is perpendicular to a side of a triangle at its midpoint.

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

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 ratio of 2:1.

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 length of a median in a triangle?

Back

To find the length of a median, use the formula: m = √(2a² + 2b² - c²) / 4, 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 difference between a median and an altitude?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude is a segment from a vertex perpendicular to the opposite side.