Angle Bisector Worksheet

Grade 12 Math worksheet on angle bisectors, covering definitions, properties, and applications in geometry.

Grade 12 Math GeometryAngle Bisector

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Includes

Multiple ChoiceFill in the BlanksShort AnswerTrue / FalseLong Answer

Standards

CCSS.MATH.CONTENT.HSG.CO.C.9CCSS.MATH.CONTENT.HSG.SRT.B.5

Topics

GeometryAngle BisectorHigh School MathGrade 12

7 sections · Free to use · Printable

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. Which of the following statements about an angle bisector is true?

It divides an angle into two unequal angles.

Every point on the angle bisector is equidistant from the two sides of the angle.

It is always perpendicular to the angle's vertex.

It only exists for right angles.

2. In triangle ABC, if AD is the angle bisector of angle A, then according to the Angle Bisector Theorem, the ratio BD/DC is equal to:

AB/AC

AC/AB

BC/AD

AD/BC

1. An angle bisector is a ray that divides an angle into two angles.

2. The intersection point of the three angle bisectors of a triangle is called the .

1. Draw an angle ∠XYZ and construct its angle bisector using a compass and straightedge. Explain the steps.

2. In a triangle ABC, if the angle bisector of ∠A intersects BC at D, and AB = 8 cm, AC = 12 cm, and BC = 10 cm, find the lengths of BD and DC.

1. The angle bisector of an angle is always perpendicular to the opposite side of the triangle.

True

False

2. The incenter of a triangle is equidistant from all three vertices of the triangle.

True

False

1. Consider a triangle ABC with vertices A(1, 5), B(-2, 1), and C(4, 1). Find the equation of the angle bisector of angle A.

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