Special Lines in Triangles: Bisectors, Medians, and Altitudes

The video tutorial explores various lines and points associated with triangles, including perpendicular bisectors, angle bisectors, medians, and altitudes. It explains the properties and significance of the circumcenter, incenter, centroid, and orthocenter, and how these points relate to different types of triangles. The tutorial also covers the concepts of circumscribed and inscribed circles, providing a comprehensive understanding of triangle geometry.

What is a perpendicular bisector in a triangle?

• A line that cuts an angle in half

• A line that is perpendicular to a side and divides it into two equal parts

• A line that extends from a vertex to the opposite side at any angle

• A line that connects a vertex to the midpoint of the opposite side

Where is the circumcenter located in an obtuse triangle?

• At the midpoint of a side

• Outside the triangle

• On the triangle

• Inside the triangle

What is the incenter of a triangle?

• The point where the medians meet

• The point where the angle bisectors meet

• The point where the perpendicular bisectors meet

• The point where the altitudes meet

How is a median of a triangle defined?

• A line that is perpendicular to a side

• A line that extends from a vertex to the opposite side at any angle

• A line that cuts an angle in half

• A line segment connecting a vertex to the midpoint of the opposite side

What is the centroid of a triangle?

• The point where the altitudes meet

• The point where the perpendicular bisectors meet

• The point where the angle bisectors meet

• The point where the medians meet

What is an altitude in a triangle?

• A line that cuts an angle in half

• A line that is perpendicular to a side and divides it into two equal parts

• A line that connects a vertex to the midpoint of the opposite side

• A line segment from a vertex perpendicular to the opposite side

Where do the altitudes of a triangle meet?

• At the circumcenter

• At the centroid

• At the incenter

• At the orthocenter