Question

if two lines interact each other, then​

Answer 1

$\huge\tt{\underline{Theorem : }}$

If two lines interact each other, then

$\huge\tt{\underline{Answer :- }}$

Data: the statement above, it is given that ‘two lines intersect each other’. So, let AB and CD be two lines intersecting at O as shown in Fig. 6.8. They lead to two pairs of vertically opposite angles, namely,

(i) ∠ AOC and ∠ BOD (ii) ∠ AOD and ∠ BOC.

Proof :

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

Explanation-

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 = ∠BOC

Answer 2

Answer:

THEOREM:-

If two lines interact each other, then

Answer:−

Data: the statement above, it is given that ‘two lines intersect each other’. So, let AB and CD be two lines intersecting at O as shown in Fig. 6.8. They lead to two pairs of vertically opposite angles, namely,

(i) ∠ AOC and ∠ BOD (ii) ∠ AOD and ∠ BOC.

Proof :

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

Explanation-

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 = ∠BOC