Understanding Angle Bisectors

What is an angle bisector?

• An angle bisector is a point where two angles meet.

• An angle bisector is a line that measures the size of an angle.

• An angle bisector is a line or ray that divides an angle into two equal angles.

• An angle bisector is a line that extends from the vertex to the opposite side.

How do you construct an angle bisector using a compass and straightedge?

• Draw a perpendicular line from the vertex to the opposite side.

• Connect the two rays of the angle with a straight line.

• Use a protractor to measure and divide the angle in half.

• To construct an angle bisector, draw a line from the vertex of the angle through the intersection of two arcs drawn from the angle's rays.

If angle A measures 60 degrees, what is the measure of each angle formed by its bisector?

• 15 degrees

• 45 degrees

• 75 degrees

• 30 degrees

Explain the Angle Bisector Theorem.

• The Angle Bisector Theorem states that the lengths of the segments created by the angle bisector are always equal.

• The Angle Bisector Theorem states that the angle bisector divides the triangle into two equal angles.

• The Angle Bisector Theorem states that the ratio of the lengths of the two segments created by the angle bisector is equal to the ratio of the lengths of the other two sides of the triangle.

• The Angle Bisector Theorem applies only to right triangles and not to other types of triangles.

If a triangle has angles of 40 degrees and 100 degrees, what is the measure of the third angle?

• 60 degrees

• 80 degrees

• 40 degrees

• 120 degrees

Draw an angle and its bisector. Label the angles.

• Angle B with bisector creating angles B1 and B2.

• Angle A with bisector creating angles A1 and A2.

• Angle C with no bisector labeled.

• Angle D with bisector creating one angle D1.

If the angle bisector divides an angle of 80 degrees, what are the measures of the two angles?

• 20 degrees and 60 degrees

• 45 degrees and 35 degrees

• 30 degrees and 50 degrees

• 40 degrees and 40 degrees

How can you use an angle bisector to find the incenter of a triangle?

• The incenter is found at the centroid of the triangle.

• The incenter is located outside the triangle.

• The incenter is the midpoint of the longest side.

• The incenter of a triangle is found at the intersection of its angle bisectors.

If the angle bisector of angle B divides it into two angles of 30 degrees and 50 degrees, what is the measure of angle B?

• 70 degrees

• 90 degrees

• 80 degrees

• 100 degrees

What is the relationship between the lengths of the segments created by an angle bisector in a triangle?

• The lengths of the segments are always the same as the lengths of the triangle's sides.

• The angle bisector creates segments that are inversely proportional to the triangle's sides.

• The lengths of the segments created by an angle bisector are proportional to the lengths of the other two sides of the triangle.

• The segments are equal in length regardless of the triangle's sides.