Triangle Properties and Centers

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 like the circumcenter, incenter, centroid, and orthocenter, and their properties. The video also covers the concepts of circumscribed and inscribed circles in triangles.

What is a perpendicular bisector in a triangle?

• 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 parts

• A line that cuts an angle in half

• 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?

• Orthocenter

• Circumcenter

• Centroid

• 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

Which point is always inside the triangle?

• None of the above

• Circumcenter

• Orthocenter

• Incenter

What is a median in a triangle?

• A line that cuts an angle in half

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

• 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 medians of a triangle meet?

• Orthocenter

• Circumcenter

• Centroid

• Incenter

What is the centroid 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

What is an altitude in a triangle?

• A line that cuts an angle in half

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

• 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

Where do the altitudes of a triangle meet?

• Circumcenter

• Orthocenter

• Centroid

• Incenter

Which point is equidistant from the sides of a triangle?

• Orthocenter

• Incenter

• Centroid

• Circumcenter