Exploring Perpendicular and Angle Bisectors in Triangles

The video tutorial covers the concepts of triangle medians, centroids, angle bisectors, incenter, and circumcenter using Geogebra. It explains how medians connect vertices to midpoints, forming centroids, and how angle bisectors intersect to form the incenter. The tutorial also demonstrates creating a circumcenter by using perpendicular bisectors, allowing the triangle to be inscribed in a circle. The video provides practical examples and visualizations to enhance understanding.

What is the centroid of a triangle?

• The point where the altitudes intersect

• The point where the perpendicular bisectors meet

• The point where the medians intersect

• The point where the angle bisectors meet

What is a median in a triangle?

• A line segment that is perpendicular to a side

• A line segment that bisects an angle

• A line segment from a vertex to the opposite vertex

• A line segment from a vertex to the midpoint of the opposite side

What is the incenter of a triangle?

• The point where the altitudes intersect

• The point where the medians intersect

• The point where the perpendicular bisectors intersect

• The point where the angle bisectors intersect

What tool is used to find the incenter in GeoGebra?

• Angle bisector tool

• Median tool

• Perpendicular bisector tool

• Altitude tool

How can you remove extra lines in GeoGebra when finding the incenter?

• Change the color of the lines to white

• Hide the lines using the hide tool

• Move the lines outside the view

• Delete the lines directly

What property does the incenter have regarding the sides of the triangle?

• It is equidistant from all three vertices

• It is the midpoint of the hypotenuse

• It is equidistant from all three sides

• It bisects the angles of the triangle

What is the circumcenter of a triangle?

• The point where the altitudes intersect

• The point where the medians intersect

• The point where the perpendicular bisectors intersect

• The point where the angle bisectors intersect

What is a perpendicular bisector in a triangle?

• A line segment that bisects an angle

• A line segment that connects two midpoints

• A line segment from a vertex to the midpoint of the opposite side

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

What unique property does the circumcenter have?

• It bisects the angles of the triangle

• It is the midpoint of the hypotenuse

• It is equidistant from all three sides

• It is equidistant from all three vertices

Where is the circumcenter located in an obtuse triangle?

• At the centroid

• Outside the triangle

• Inside the triangle

• On the hypotenuse