Triangle Centers and Properties

The video tutorial explains the four types of concurrent lines in a triangle: medians, perpendicular bisectors, angle bisectors, and altitudes. It describes how each type of line is constructed and their significance, such as the centroid, circumcenter, incenter, and orthocenter. The video also covers special cases for right, acute, and obtuse triangles, highlighting the positions of these points within or outside the triangle.

What are the four types of concurrent lines in a triangle?

• Medians, Angle Bisectors, Altitudes, Diagonals

• Medians, Perpendicular Bisectors, Altitudes, Diagonals

• Medians, Perpendicular Bisectors, Angle Bisectors, Diagonals

• Medians, Perpendicular Bisectors, Angle Bisectors, Altitudes

What is the line called that connects a vertex of a triangle to the midpoint of the opposite side?

• Angle Bisector

• Perpendicular Bisector

• Median

• Altitude

Where do the three medians of a triangle intersect?

• Orthocenter

• Centroid

• Incenter

• Circumcenter

What is the ratio in which the centroid divides each median?

• 1:2

• 3:1

• 2:1

• 1:1

What is a perpendicular bisector in a triangle?

• A line that is parallel to one side of the triangle

• A line that bisects a side and is perpendicular to it

• A line that bisects an angle into two equal parts

• A line that connects a vertex to the midpoint of the opposite side

What is the point called where the perpendicular bisectors of a triangle meet?

• Orthocenter

• Circumcenter

• Centroid

• Incenter

In a right triangle, where is the circumcenter located?

• At the vertex of the right angle

• At the midpoint of the hypotenuse

• Inside the triangle

• Outside the triangle

In an obtuse triangle, where is the circumcenter located?

• At the vertex of the obtuse angle

• At the midpoint of the longest side

• Outside the triangle

• Inside the triangle

What is an angle bisector in a triangle?

• A line that bisects an angle into two equal parts

• A line that is parallel to one side of the triangle

• A line that connects a vertex to the midpoint of the opposite side

• A line that bisects a side and is perpendicular to it

Where do the angle bisectors of a triangle intersect?

• Centroid

• Incenter

• Circumcenter

• Orthocenter