Triangle Centers and Properties

Professor Dave explains various lines and points associated with triangles, including perpendicular bisectors, angle bisectors, medians, and altitudes. He describes how these lines intersect at specific points: the circumcenter, incenter, centroid, and orthocenter. Each point has unique properties, such as being equidistant from certain parts of the triangle. The video also covers how these concepts can be used to prove geometric theorems.

What is a line that is perpendicular to one side of a triangle and divides it into two equal parts called?

• Altitude

• Median

• Perpendicular bisector

• Angle bisector

If a perpendicular bisector coincides with the other two sides of a triangle, what type of triangle is formed?

• Scalene triangle

• Right triangle

• Isosceles triangle

• Equilateral triangle

What is the line called that divides an angle into two equal parts?

• Median

• Altitude

• Angle bisector

• Perpendicular bisector

Where do the three perpendicular bisectors of a triangle meet?

• Incenter

• Centroid

• Orthocenter

• Circumcenter

In which type of triangle is the circumcenter located outside the triangle?

• Equilateral triangle

• Acute triangle

• Right triangle

• Obtuse triangle

What is the center of the circle that circumscribes a triangle called?

• Centroid

• Incenter

• Orthocenter

• Circumcenter

Where do the angle bisectors of a triangle meet?

• Circumcenter

• Orthocenter

• Centroid

• Incenter

What is the center of the circle that is inscribed in a triangle called?

• Incenter

• Orthocenter

• Centroid

• Circumcenter

What is a line segment that connects a vertex to the midpoint of the opposite side called?

• Angle bisector

• Perpendicular bisector

• Median

• Altitude

Where do the medians of a triangle meet?

• Orthocenter

• Circumcenter

• Centroid

• Incenter