Mathematics

# If two straight lines intersect each other, then prove that the ray opposite to the bisector of one of the angles so formed bisects the vertically opposite angle.

##### SOLUTION
Let us consider $AB$ and $CD$ as the two lines intersecting at a point $O$ where $OE$ is the ray bisecting $\angle BOD$ and $OF$ is the ray bisecting $\angle AOC$

To Prove: $\angle AOF=\angle COF$

Proof: $EF$ is a straight line passing through the point $O$ where $\overrightarrow { OE }$ and $\overrightarrow { OF }$ are tow opposite rays

From the figure we know that $\angle AOF$ and $\angle BOE$, $\angle COF$ and $\angle DOE$ are vertically opposite angles

so it can be written as

$\angle AOF=\angle BOE$ and$\angle COF=\angle DOE$

it is given that $\angle BOE=\angle DOE$

so we can write it as $\angle AOF=\angle COF$

therefore it is proved that $\angle AOF=\angle COF$

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Subjective Medium Published on 09th 09, 2020
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86

#### Realted Questions

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