Triangle Properties and Centers

Professor Dave explains various lines in 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 triangle types and their geometric properties.

What is a perpendicular bisector 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 connects a vertex to the midpoint of the opposite side

• A line that divides an angle into two equal parts

Where do the perpendicular bisectors of a triangle meet?

• At the incenter

• At the centroid

• At the circumcenter

• At the orthocenter

What is true about the circumcenter of an obtuse triangle?

• It is inside the triangle

• It is outside the triangle

• It is on the triangle

• It is at the centroid

What is the incenter of a triangle?

• The point where the perpendicular bisectors meet

• The point where the altitudes meet

• The point where the angle bisectors meet

• The point where the medians meet

Which circle is associated with the incenter of a triangle?

• The median circle

• The altitude circle

• The inscribed circle

• The circumscribed circle

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 centroid

• At the orthocenter

• At the incenter

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 altitudes of a triangle meet?

• At the orthocenter

• At the circumcenter

• At the centroid

• At the incenter

Which point is always inside the triangle?

• None of the above

• Circumcenter

• Incenter

• Orthocenter