Exploring Angle Bisectors and Their Theorem

What does an angle bisector do to an angle?

• Splits it into three equal parts

• Does not split the angle

• Splits it into two equal parts

• Splits it into four equal parts

If a ray splits angle ABC into two equal angles, what is this ray called?

• Angle bisector

• Angle divider

• Angle splitter

• Angle separator

What is true about any point on the angle bisector?

• It is equidistant from the two sides of the angle

• It is closer to one side of the angle

• It is farther from one side of the angle

• It is not related to the sides of the angle

How can you prove a line is an angle bisector?

• By showing the angles on either side of the line are equal

• By showing the line is parallel to one side

• By showing the line is longer than the sides

• By showing the line is perpendicular to one side

What does the converse of the angle bisector theorem state?

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

• If a point is on the angle bisector, it is not equidistant from the sides

• If a point is closer to one side, it lies on the angle bisector

• If a point is farther from one side, it lies on the angle bisector

Which theorem helps in proving that a line is an angle bisector by showing equidistant points?

• Triangle Inequality Theorem

• Converse of the Angle Bisector Theorem

• Angle Bisector Theorem

• Pythagorean Theorem

What is the incenter of a triangle?

• The point where the angle bisectors meet

• The point where the perpendicular bisectors meet

• The point where the altitudes meet

• The point where the medians meet

What is the significance of the incenter in a triangle?

• It is the midpoint of the shortest side

• It is the midpoint of the longest side

• It is the center of the inscribed circle

• It is the center of the circumscribed circle

What do you call the point where the perpendicular bisectors of a triangle meet?

• Incenter

• Circumcenter

• Orthocenter

• Centroid

What is the relationship between the incenter and the sides of the triangle?

• The incenter is equidistant from the sides

• The incenter is equidistant from the vertices

• The incenter is closer to one side

• The incenter is farther from one side