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 overview of triangle geometry.

What is a perpendicular bisector in a triangle?

• A line that extends from a vertex to the opposite side at a right 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 three perpendicular bisectors of a triangle meet?

• At the orthocenter

• At the centroid

• At the circumcenter

• At the incenter

What is the incenter of a triangle?

• The point where the medians meet

• The point where the angle bisectors 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 is the centroid of a triangle located?

• Always outside the triangle

• Always inside the triangle

• At the midpoint of the longest side

• On the hypotenuse of a right triangle

What is the orthocenter of a triangle?

• The point where the medians meet

• The point where the angle bisectors meet

• The point where the altitudes meet

• The point where the perpendicular bisectors meet

How many altitudes does a triangle have?

• Four

• One

• Three

• Two

Which point is equidistant from the vertices of a triangle?

• Orthocenter

• Incenter

• Circumcenter

• Centroid

Which point is equidistant from the sides of a triangle?

• Orthocenter

• Centroid

• Circumcenter

• Incenter

What is the significance of the centroid in a triangle?

• It is the center of the circumscribed circle

• It is the point where the altitudes meet

• It is the center of the inscribed circle

• It divides each median into a 2:1 ratio