Question

Given: is an angle bisector of ∠JMKProve: m

Answer 1

Answer:

An angle bisector is a line passing through the vertex of the angle that cuts the angle into two equal smaller angles.

Given: MN is angle bisector,

then  

$\angle JMN \cong \angle NMK$            .......  [1]

Congruent angles are  two or more angles that have the same measure.

then;

by definition of congruent angles

[1]⇒ $m\angle JMN = m\angle NMK$                ......[2]

By the  Angle addition postulates states that if M is in the interior of ∠JMK then,

$m\angle JMN+m\angle NMK =m\angle JMK$            ......[3]

Now, by substitution property ; substitute the equation [2] in [3] we get;

$m\angle JMN+m\angle JMN =m\angle JMK$                 ......[4]

Like terms terms whose variables  are the same

Combine like terms in equation [4] we get

$2 \cdot m\angle JMN=m\angle JMK$                      ......[5]

Division property of equality states that you divide the same number to both sides of an equation.

Divide by 2 to both sides in equation [5] , we get

$m\angle JMN= \frac{1}{2} m\angle JMK$