Question

State whether the following axioms are True or False:

If two lines intersect each other, then the vertically opposite angles are not equal.

• A. True
• B. False

Answer 1

The correct option is B False

The following axiom is false because

"If two lines intersect each other , then the vertically opposite angles are equal"

we can show it by taking an example :

$\angle POR=\angle QOS$ $\angle POS=\angle ROQ$

let PQ and RS intersect each other then we show that vertically oppposite angles i.e

now ray OP is on RS

$\angle POR+\angle POS$=180-------------1 (linear pair axioms)

simillarly

$\angle POR+\angle QOS$=180------------2

from 1 and 2

$\angle POS+\angle QOS$=$\angle POR+\angle POS$

or

$\angle POR+\angle QOS$

similarly

$\angle POS+\angle ROQ$