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 certain parts of the triangle. The video 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 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

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

Where do the three perpendicular bisectors of a triangle meet?

• At the incenter

• At the orthocenter

• 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 equidistant from the sides of the triangle

• It is the center of the inscribed circle

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 equidistant from the vertices

• It is equidistant from the sides

• It is always outside the triangle

• It is the center of the circumscribed circle

What is a median in a triangle?

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

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

• 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 incenter

• At the centroid

• At the orthocenter

• At the circumcenter

What is the orthocenter of a triangle?

• The point where the medians meet

• The point where the perpendicular bisectors meet

• The point where the altitudes meet

• The point where the angle bisectors meet

Which of the following is true about the centroid?

• It is two-thirds of the way from a vertex to the midpoint of the opposite side

• It is the center of the circumscribed circle

• It is equidistant from the sides

• It is always outside the triangle

What is an altitude in a triangle?

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

• A line that divides an angle into two equal parts

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

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