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, altitudes, angle bisectors, and perpendicular bisectors that have specific properties and roles in triangle geometry.

Front

Define a median in a triangle.

Back

A median is a 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

Define 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 segment that divides an angle into two equal angles.

Front

If AD and DC are congruent sides, what can be inferred about triangle ABC?

Back

Triangle ABC is isosceles with sides AD and DC being equal.

Front

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

Back

Use properties of congruence, similarity, or the Pythagorean theorem, depending on the triangle's characteristics.

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

Front

How can you identify an altitude in a triangle?

Back

An altitude can be identified as the segment that forms a right angle with the base of the triangle.