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 $$\angle AOF=\angle COF$$
View Answers

You're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!


Subjective Medium Published on 09th 09, 2020
Next Question
Questions 120418
Subjects 10
Chapters 88
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
Consider the following statements:
Two lines intersected by a transversal are parallel if:
1. the pairs of corresponding angles are equal.
2. the interior angles on the same side of the transversal are supplementary.
Which of the statements given above is/are correct?
  • A. $$1$$ only
  • B. $$2$$ only
  • C. Neither $$1$$ nor $$2$$
  • D. Both $$1$$ and $$2$$

Asked in: Mathematics - Straight Lines


1 Verified Answer | Published on 17th 08, 2020

View Answer
Q2 Subjective Medium
In the given figure, $$AB \parallel CD$$ and $$EF$$ is a transversal. If $$\angle AEF = 65^{\circ}, \angle DFG = 30^{\circ}, \angle EGF = 90^{\circ}$$ and $$\angle GEF = x^{\circ}$$, find the value of $$x$$.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 23rd 09, 2020

View Answer
Q3 Single Correct Medium
If a line is divided by three parallel lines into two-segments of lengths in the ratio 1 : 3, another line will be divided by these parallel lines into two segments of lengths in the ratio
  • A. 3 : 1
  • B. 1 : 2
  • C. 2 : 1
  • D. 1 : 3

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q4 Subjective Medium
By simply looking at the pair of angles given in figure. State which of the angle in the pairs is greater.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer
Q5 One Word Medium
Two angles forming a ________ pair are supplementary.

Asked in: Mathematics - Lines and Angles


1 Verified Answer | Published on 09th 09, 2020

View Answer