Triangle Centers and Properties

Professor Dave explains various lines and points related to triangles, including perpendicular bisectors, angle bisectors, medians, and altitudes. He describes how these lines intersect at specific points: circumcenter, incenter, centroid, and orthocenter. Each point has unique properties, such as being equidistant from vertices or sides. The video also covers the concepts of circumscribed and inscribed circles, and how these geometric principles can be used to prove properties of triangles.

What is a perpendicular bisector in a triangle?

• A line that divides an angle into two equal parts

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

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

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

Where do the three perpendicular bisectors of a triangle meet?

• At the orthocenter

• At the incenter

• At the centroid

• At the circumcenter

What is true about the circumcenter of a triangle?

• It is always inside the triangle

• It is equidistant from the vertices of the triangle

• It is the center of the inscribed circle

• It is equidistant from the sides of the triangle

What is the incenter of a triangle?

• The point where the angle bisectors meet

• The point where the medians meet

• The point where the altitudes meet

• The point where the perpendicular bisectors meet

Which statement is true about the incenter?

• It is the center of the circumscribed circle

• It is equidistant from the vertices

• It is always outside the triangle

• It is equidistant from the sides

What is a median in a triangle?

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

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

• A line that divides an angle into two equal parts

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

Where do the medians of a triangle meet?

• At the orthocenter

• At the centroid

• At the circumcenter

• At the incenter

What is the centroid of a triangle?

• The point where the angle bisectors meet

• The point where the medians meet

• The point where the altitudes meet

• The point where the perpendicular bisectors meet

What is an altitude in a triangle?

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

• A line that divides an angle into two equal parts

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

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

Where do the altitudes of a triangle meet?

• At the circumcenter

• At the centroid

• At the incenter

• At the orthocenter