Question

Two straight lines AB and CD intersect at the point O. Now draw the bisectors of any one pair of vertically opposite angles. Then prove that the bisectors are on same line.​

Answer 1

Step-by-step explanation:

Let us assume that AB and CD are straight lines and these lines intersect at point 0.

Let us consider that XO is the bisector of ZAOC formed by the intersection of AB and CD. Similarly

let OY be the bisector of ZBOD.

: 23 = 4..(1

From the figure, we can say that 2 = 25, which form the vertically opposite angles. We know that the sum of all angles formed at a point is 360°

Thus, we can say that,

angle21 + angle2 + angle3 + angle24 + angle25 + angle26 = 360°