It is a line segment that passes through the vertex of an angle and divides it into two equal parts.

What is known as a bisector in a triangle?

It is the line segment that divides an interior angle of the triangle into two equal angles.

How many bisectors does a triangle have?

Remember that a triangle has three vertices, therefore, it has three bisectors.

What is the measure of the equal angles generated by the bisectors of an equilateral triangle?

Recalling that the measure of the internal angles of any equilateral triangle is $60°$, then the bisectors will divide these angles into two equal angles of $30°$ each.

The answer is C because the angle bisector divides the angle into two equal angles. In diagram C, the angle bisector divides the right angle, which is equal to 90 degrees, into 2 angles that are equal to each other. $45=45$

Answer

Exercise #2

BD is a bisector.

What is the size of angle ABC?

Video Solution

Step-by-Step Solution

Since we are given that the value of angle DBC is 65 degrees, and we know that the angle bisector divides angle ABC into two equal angles, we can calculate the value of angle ABC:

$65+65=130$

Answer

130

Exercise #3

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

Video Solution

Step-by-Step Solution

Since an angle bisector divides the angle into two equal angles, and we are given that one angle is equal to 60 degrees. Angle $\alpha$ is also equal to 60 degrees

Answer

60

Exercise #4

ABCD is a square.

$∢\text{ABC}=\text{?}$

Video Solution

Step-by-Step Solution

Since in a square all angles are equal to 90 degrees, and BC bisects an angle, we can calculate angle ABC:

$90:2=45$

Answer

45

Exercise #5

ABCD is a deltoid.

$∢DAC=\text{?}$

Video Solution

Step-by-Step Solution

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

$BAC=CAD=2X$

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:

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

$6X+60=180$

$180-60=6X$

$120=6X$

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