the angles form a line.For obvious reasons, the two axioms above toget

1.	the angles form a line.For obvious reasons, the two axioms above together is called theLineiomLet us now examine the case when two lines intersect each other.Recall, from earlier classes, that when two lines intersect, the verticallyare equal. Let us prove this result now. See Appendix 1 for the ingredi, and keep those in mind while studying the proof given below.rem 6.1 : If two lines intersect each other, then the verticallys are equal.: In the statement above, it is givenvo lines intersect each other'. So, letCD be two lines intersecting at O asn Fig. 6.8. They lead to two pairs ofy opposite angles, namelyC and 2 BOD (ii) < AOD andesFig. 6.8:Vertically opposite
Answer» We need to prove that ∠ AOC = ∠ BOD and ∠ AOD = ∠ BOC. Now, ray OA stands on line CD. Therefore, ∠ AOC + ∠ AOD = 180° (Linear pair axiom) ………..(1) Can we write ∠ AOD + ∠ BOD = 180°? (Linear pair axiom)……………(2) From (1) and (2), we can write ∠ AOC + ∠ AOD = ∠ AOD + ∠ BOD This implies that ∠ AOC = ∠ BOD Similarly, it can be proved that ∠AOD = ∠BOCClick to let others know, how helpful is it cob =aod vertically opposite angle

the angles form a line.For obvious reasons, the two axioms above together is called theLineiomLet us now examine the case when two lines intersect each other.Recall, from earlier classes, that when two lines intersect, the verticallyare equal. Let us prove this result now. See Appendix 1 for the ingredi, and keep those in mind while studying the proof given below.rem 6.1 : If two lines intersect each other, then the verticallys are equal.: In the statement above, it is givenvo lines intersect each other'. So, letCD be two lines intersecting at O asn Fig. 6.8. They lead to two pairs ofy opposite angles, namelyC and 2 BOD (ii) < AOD andesFig. 6.8:Vertically opposite

Answer»

We need to prove that ∠ AOC = ∠ BOD and ∠ AOD = ∠ BOC.

Now, ray OA stands on line CD.

Therefore, ∠ AOC + ∠ AOD = 180° (Linear pair axiom) ………..(1)

Can we write ∠ AOD + ∠ BOD = 180°? (Linear pair axiom)……………(2)

From (1) and (2), we can write

∠ AOC + ∠ AOD = ∠ AOD + ∠ BOD

This implies that ∠ AOC = ∠ BOD

Similarly, it can be proved that ∠AOD = ∠BOCClick to let others know, how helpful is it

cob =aod vertically opposite angle