Exploring Angle Bisectors and Their Theorems

This video tutorial covers the concept of angle bisectors, explaining that an angle bisector is a line, segment, or ray that divides an angle into two congruent angles. It discusses the property that any point on an angle bisector is equidistant from the two sides of the angle. The video also explores the converse property, where a line with a point equidistant from the angle's sides is an angle bisector. Additionally, the tutorial examines the intersection of angle bisectors in a triangle, forming the incenter, which is equidistant from all triangle sides and serves as the center of an inscribed circle.

What is an angle bisector?

• A line that is perpendicular to one side of an angle

• A line that is parallel to one side of an angle

• A line that divides an angle into two equal parts

• A line that divides an angle into two unequal parts

What happens to the two angles formed by an angle bisector?

• They become supplementary

• They become congruent

• They become complementary

• They become right angles

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

• It is closer to one side than the other

• It is equidistant from both sides

• It is farther from one side than the other

• It is not related to the sides

What must be true for a point on an angle bisector to be equidistant from the sides of the angle?

• The point must be at the vertex of the angle

• The point must be on the perpendicular bisector of the angle

• The point must be on the angle bisector

• The point must be outside the angle

What does the converse property of angle bisectors state?

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

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

• If a point is equidistant from the sides of an angle, it lies on the angle itself

• If a point is equidistant from the sides of an angle, it lies outside the angle

What happens when you construct the angle bisectors of all three angles in a triangle?

• They intersect at a single point

• They do not intersect

• They form a right triangle

• They intersect at three different points

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

• Centroid

• Incenter

• Circumcenter

• Orthocenter

Where is the incenter of a triangle always located?

• At the vertex of the triangle

• Inside the triangle

• On one of the sides of the triangle

• Outside the triangle

What is the incenter of a triangle the center of?

• A circle that is tangent to one side of the triangle

• A circle that passes through all three vertices of the triangle

• A circle that is circumscribed around the triangle

• A circle that is inscribed in the triangle

What is true about the distances from the incenter to the sides of the triangle?

• They are all infinite

• They are all zero

• They are all equal

• They are all different