Exploring Angle Bisectors in Triangles

This video tutorial reviews the properties of angle bisectors in a triangle. It explains how each angle bisector divides an angle into two congruent angles and introduces the concept of the incenter, the point where all angle bisectors intersect. The incenter is equidistant from the triangle's sides, allowing the construction of an inscribed circle. The video concludes with the Concurrency of Angle Bisectors Theorem, emphasizing that the distance from the incenter to the sides is measured perpendicularly.

How many angle bisectors does a triangle have?

• Two

• One

• Four

• Three

What does ray CE do to angle ACB?

• Makes it smaller

• Bisects it into two congruent angles

• Divides it into three equal parts

• Makes it larger

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

• Orthocenter

• Incenter

• Circumcenter

• Centroid

What is the incenter equidistant from?

• The vertices of the triangle

• The sides of the triangle

• The angles of the triangle

• The midpoints of the sides

How is the distance from the incenter to a side of the triangle measured?

• Along the side of the triangle

• Along the median

• Perpendicularly to the side

• Along the angle bisector

What shape can be constructed inside the triangle using the incenter?

• A circle

• A hexagon

• A rectangle

• A square

What is the circle called that is centered at the incenter?

• Incircle

• Excircle

• Inscribed circle

• Circumscribed circle

What does the Concurrency of Angle Bisectors Theorem state?

• The angle bisectors of a triangle intersect at the centroid

• The angle bisectors of a triangle intersect at the circumcenter

• The angle bisectors of a triangle intersect at the orthocenter

• The angle bisectors of a triangle intersect at a point equidistant from the three sides

What is the most important thing to remember about the distance from the incenter to the sides?

• It is the length of the altitude

• It is the length of the median

• It is the length of a perpendicular segment

• It is measured along the angle bisector

What will be covered in the next video?

• Constructing the angle bisectors of a triangle

• Properties of the circumcenter

• Properties of the centroid

• Properties of the orthocenter