Bisector - Examples, Exercises and Solutions

A bisector is a line segment that passes through the vertex of an angle and divides it into two equal angles.

The bisector can appear in a triangle, parallelogram, rhombus and in other geometric figures.

For example, a bisector that passes through an angle of 120° 120° degrees will create two angles of 60° 60° degrees each.

A1  -  Bisector

Suggested Topics to Practice in Advance

  1. Right angle
  2. Acute Angles
  3. Obtuse Angle
  4. Plane angle
  5. Angle Notation

Practice Bisector

Exercise #1

ABCD is a deltoid.

DAC=? ∢DAC=\text{?}

AAABBBCCCDDD2x602x

Video Solution

Step-by-Step Solution

As we know that ABCD is a deltoid, and AC is the bisector of an angle and therefore:

BAC=CAD=2X BAC=CAD=2X

Now we focus on the triangle BAD and calculate the sum of the angles since we know that the sum of the angles in a triangle is 180 degrees:

2X+2X+2X+60=180 2X+2X+2X+60=180

6X+60=180 6X+60=180

18060=6X 180-60=6X

120=6X 120=6X

We divide the two sections by 6:1206=6x6 \frac{120}{6}=\frac{6x}{6}

20=x 20=x

Now we can calculate the angle DAC:

20×2=40 20\times2=40

Answer

40

Exercise #2

Which of the following figures has a bisector?

Video Solution

Answer

4545

Exercise #3

BD is a bisector.

What is the size of angle ABC?

656565AAABBBCCCDDD

Video Solution

Answer

130

Exercise #4

Calculate the size of angle α \alpha given that it is a bisector.αααaaa

Video Solution

Answer

45

Exercise #5

Calculate angle α \alpha given that it is a bisector.

ααα606060AAAaaa

Video Solution

Answer

60

Exercise #1

Given:

ABC=90 ∢\text{ABC}=90

DBC=45 ∢DBC=45

Is BD a bisector?

AAABBBCCCDDD45

Video Solution

Answer

Yes

Exercise #2

ABD=15 ∢\text{ABD}=15

BD bisects the angle.

Calculate the size of ABC ∢\text{ABC} .

AAABBBCCCDDD15

Video Solution

Answer

30

Exercise #3

ABD=90 ∢\text{ABD}=90

CB bisects ABD \sphericalangle\text{ABD} .

CBD=α \sphericalangle\text{CBD}=\alpha

Calculate the size of ABC ∢ABC .

AAABBBDDDCCCα

Video Solution

Answer

45

Exercise #4

ABC=120 ∢ABC=120

ABD=60 ∢ABD=60

Which of the following are true?

AAABBBCCCDDD60120

Video Solution

Answer

BD bisects ABC ∢ABC .

Exercise #5

DBC=90° ∢DBC=90°

BE cross DBA ∢\text{DBA}

Find the value α \alpha

AAABBBCCCDDDEEEα

Video Solution

Answer

45

Exercise #1

BO bisects ABD ∢ABD .

ABD=85 ∢\text{ABD}=85

Calculate the size of

ABO. \sphericalangle ABO\text{.} 85°85°85°AAACCCBBBOOODDD

Video Solution

Answer

42.5

Exercise #2

What is the size of angle ABC given that BD is a bisector?

AAABBBCCCDDD40

Video Solution

Answer

80

Exercise #3

ABC =130 ∢ABC\text{ }=130

Given that a is a bisector, calculate angle α \alpha .

αααaaaAAABBBCCC

Video Solution

Answer

65

Exercise #4

a is a bisector.

BAC=80° ∢BAC = 80°

Calculate angle α \alpha .

αααaaaAAABBBCCC

Video Solution

Answer

40

Exercise #5

The triangle ABC is shown below.

CD bisects C.

Angle C equals 122 degrees.

Calculate angle ACD ∢\text{ACD} .AAABBBCCCDDD

Video Solution

Answer

61°

Topics learned in later sections

  1. The Sum of the Interior Angles of a Triangle
  2. Sides, Vertices, and Angles
  3. Types of Angles
  4. Sum and Difference of Angles
  5. Sum of Angles in a Polygon
  6. Exterior angle of a triangle