Understanding Angle Bisectors in Triangles

This video tutorial explains how to construct the angle bisectors of a triangle using a compass and straight edge. It covers the process for each vertex, demonstrating how to create congruent angles by bisecting the interior angles. The tutorial also discusses the point of concurrency, known as the incenter, which is equidistant from the triangle's sides. The video concludes with the concurrency of angle bisector theorem, stating that the angle bisectors intersect at a point equidistant from the triangle's sides.

What tools are necessary to construct the angle bisectors of a triangle?

• Compass and straight edge

• Ruler and pencil

• Protractor and ruler

• Calculator and pencil

What is the first step in constructing the angle bisector for angle A?

• Draw a circle around the triangle

• Measure the angle with a protractor

• Place the compass at vertex A and swing an arc

• Draw a straight line

After swinging the first arc at vertex A, what should you do next?

• Swing another arc at vertex B

• Change the radius of the compass

• Draw a line through the arc

• Measure the arc length

What is the result of bisecting angle A?

• A right angle

• Two congruent angles

• An obtuse angle

• Two unequal angles

How do you ensure the angle bisector for angle B is accurate?

• Draw a circle around the angle

• Use a ruler to draw the bisector

• Measure the angle with a protractor

• Swing arcs from both intersection points

What is the significance of the point where angle bisectors intersect?

• It is the centroid

• It is the orthocenter

• It is the incenter

• It is the circumcenter

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

• It is the shortest distance from the vertices

• It is equidistant from the vertices

• It is equidistant from the sides

• It is the longest distance from the sides

What can be constructed using the incenter of a triangle?

• A square

• A rectangle

• A tangent line

• An inscribed circle

What does the concurrency of angle bisectors theorem state?

• Angle bisectors form a right angle

• Angle bisectors intersect at a point equidistant from the sides

• Angle bisectors intersect at the centroid

• Angle bisectors are parallel

What is the relationship between the incenter and the inscribed circle?

• The incenter is on the circle

• The incenter is the center of the circle

• The incenter is outside the circle

• The incenter is tangent to the circle