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: circumcenter, incenter, centroid, and orthocenter, each with unique properties. The video covers how these concepts relate to different types of triangles and their geometric properties.

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 a right angle

Where do the three perpendicular bisectors of a triangle meet?

• At the circumcenter

• At the orthocenter

• At the centroid

• At the incenter

What is the circumcenter 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

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

What is a median 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 a right angle

Where do the three medians of a triangle meet?

• At the circumcenter

• At the incenter

• At the centroid

• At the orthocenter

What is the centroid of a triangle?

• The point where the angle bisectors meet

• The point where the medians meet

• The point where the perpendicular bisectors meet

• The point where the altitudes meet

What is an altitude 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 a right angle

Where do the three altitudes of a triangle meet?

• At the incenter

• At the orthocenter

• At the centroid

• At the circumcenter

Which point is always inside the triangle?

• None of the above

• Orthocenter

• Incenter

• Circumcenter