Exploring Angle Bisectors and the Incenter

This video tutorial by Mr. Math Log covers the concept of angle bisectors in triangles, explaining how to construct them using a compass and straightedge. It introduces the in-center, a point equidistant from all sides of a triangle, and discusses the in-center theorem. The lesson also covers the angle bisector theorem, providing examples and problems to illustrate its application. The tutorial concludes with a summary and a homework assignment for further practice.

What is the point called where the angle bisectors of a triangle intersect?

• Circumcenter

• Orthocenter

• In-center

• Centroid

What tool is NOT necessary for constructing an angle bisector?

• Compass

• Protractor

• Pencil

• Straightedge

What is the significance of the in-center in a triangle?

• It is equidistant from all the vertices.

• It is the midpoint of the longest side.

• It is equidistant from all the sides.

• It is the center of the circumscribed circle.

What is the term for the point where three or more lines intersect?

• Centroid

• Circumference

• Concurrent

• Orthocenter

If the distance from the in-center to one side of the triangle is 7.3 units, what is the distance to the other sides?

• 14.6 units

• It varies

• 3.65 units

• 7.3 units

If an angle bisector divides an angle of 112 degrees, what is the measure of each resulting angle?

• 56 degrees

• 112 degrees

• 28 degrees

• 84 degrees

What is the measure of each angle if an angle bisector divides a 36-degree angle?

• 18 degrees

• 36 degrees

• 72 degrees

• 9 degrees

What does the angle bisector theorem state?

• The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices.

• The medians of a triangle intersect at a point that is equidistant from the sides.

• The angle bisectors of a triangle intersect at a point that is equidistant from the sides.

• The angle bisectors of a triangle intersect at a point that is equidistant from the vertices.

If a point lies on the angle bisector, what can be said about its distance to the sides of the angle?

• It is closer to one side.

• It is equidistant to the sides.

• It is farther from one side.

• It is at the midpoint of the angle.

What is the converse of the angle bisector theorem?

• If a point is equidistant to the sides of an angle, it lies on the angle bisector.

• If a point is equidistant to the sides of an angle, it lies on the perpendicular bisector.

• If a point is equidistant to the sides of a triangle, it lies on the perpendicular bisector.

• If a point is equidistant to the vertices of a triangle, it lies on the angle bisector.