Special Segments in Triangles

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle. It is parallel to the third side and its length is half the length of that side.

Front

What is the relationship between a triangle's median and its sides?

Back

A median of a triangle is a line segment that connects a vertex to the midpoint of the opposite side. Each triangle has three medians, and they intersect at a point called the centroid.

Front

Define an angle bisector in a triangle.

Back

An angle bisector is a line segment that divides an angle into two equal angles. In a triangle, each vertex has an angle bisector.

Front

What is the purpose of a perpendicular bisector in a triangle?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a right angle. It can be used to find the circumcenter of a triangle.

Front

How do you find the length of a midsegment?

Back

The length of a midsegment is half the length of the side it is parallel to.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is also the center of mass of the triangle.

Front

Explain the concept of a triangle's altitude.

Back

An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side. It represents the height of the triangle.

Front

What is the difference between a median and an altitude in a triangle?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude connects a vertex to the opposite side at a right angle.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is the center of the circumcircle that passes through all three vertices.

Front

How do you identify a midsegment in a triangle?

Back

A midsegment can be identified as the segment connecting the midpoints of two sides of a triangle.