Angle Bisector Worksheet
A Grade 9 math worksheet focusing on understanding and constructing angle bisectors, including problems involving angle measures.
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Angle Bisector Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work where applicable. For construction problems, use a compass and straightedge.
1. What is the definition of an angle bisector?
A line segment that connects two non-adjacent vertices of a polygon.
A ray that divides an angle into two congruent angles.
A line that intersects a segment at its midpoint.
A segment that is perpendicular to another segment.
2. If ray BD bisects ∠ABC and m∠ABC = 70°, what is m∠ABD?
30°
35°
70°
140°
3. An angle bisector divides an angle into two angles.
4. The distance from any point on an angle bisector to the two sides of the angle is .
5. Construct the angle bisector of the angle shown below. You may use a protractor to verify your construction.
6. In the diagram below, ray QS bisects ∠PQR. If m∠PQS = (3x + 5)° and m∠SQR = (2x + 15)°, find the value of x and m∠PQR.
7. Every angle has exactly one angle bisector.
True
False
8. An angle bisector always forms a right angle with the sides it bisects.
True
False
9. Given an angle ∠XYZ, describe the steps to construct its angle bisector using only a compass and straightedge.
10. An angle measures 120°. If it is bisected, and then one of the resulting angles is bisected again, what are the measures of the three angles formed?
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