Question

If two lines intersect,prove that the vertically opposite angles are equal

Answer 1

Explanation:

LOM and PON be two lines

LOP + POM = 180° .....(linear pair)

POM + MON = 180° .....(linear pair angle)

So,

LOP + POM =POM + MON

LOP = MON.....(eliminating POM)

hence proved

similarly you can prove other side also

Answer 2

we can only answer the question if we know the name of two lines and the name of the point where the two line intersects .

Let put the name of first line as line AB the name of second line as CD and there intersecting point at point O as shown in the figure.

They lead to two pairs of vertically opposite angles, namely,

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

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

I hope it will help you .

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