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 with unique properties. The video covers how these concepts help in understanding triangle properties and solving geometric problems.

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 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 do the three perpendicular bisectors of a triangle meet?

• At the incenter

• At the circumcenter

• At the orthocenter

• At the centroid

What is true about the circumcenter of a triangle?

• It is the center of the inscribed circle

• It is equidistant from the sides of the triangle

• It is equidistant from the vertices of the triangle

• It is always inside the triangle

What is the incenter of a triangle?

• The point where the altitudes meet

• The point where the perpendicular bisectors meet

• The point where the medians meet

• The point where the angle bisectors meet

Which statement is true about the incenter?

• It is the center of the circumscribed circle

• It is equidistant from the vertices of the triangle

• It is equidistant from the sides of the triangle

• It is always outside the triangle

What is a median in a triangle?

• 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

• 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

Where do the medians of a triangle meet?

• At the circumcenter

• At the incenter

• At the orthocenter

• At the centroid

What is the orthocenter of a triangle?

• The point where the altitudes meet

• The point where the medians meet

• The point where the angle bisectors meet

• The point where the perpendicular bisectors meet

Which of the following is true about the centroid?

• It is the center of the circumscribed circle

• It is always outside the triangle

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

• It is equidistant from the sides of the triangle

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