Question

prove that the bisector of a pair of vertically opposite angles are in the same straight line

Answer 1

Hey

Here is your answer,


/AOC – /BOO

Also OE is the bisector of ADC and OF is the bisector of BOD

To prove: EOF is a straight line, vertically opposite angles are equal

AOD = BOC = 5x —–(1)

Also ,

AOC +BOD

2 AOD = 2 DOF —–(2)
We know,

Sum of the angles around a point is 360

2 AOD + 2 AOE + 2 DOF = 360
AOD + AOE + DOF = 180
From this we can conclude that EOF is a straight line.

Given that: – AB and CD intersect each other at O

OE bisects COB

To prove: AOF = DOF

Proof: OE bisects COB

COE = EOB = x

Vertically opposite angles are equal

BOE = AOF = x —– (1)
COE = DOF= x —– (2)
From (1) and (2),
Aof = dof = x

Hence Proved.

Hope it helps you!