Prove that if two lines intersect each other then vertically opposite angles are equal.

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Prove that if two lines intersect each other then vertically opposite angles are equal.

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1 week 2021-10-07T13:05:14+00:00 1 Answer 0 views 0

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    2021-10-07T13:06:24+00:00

    Step-by-step explanation:

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

    Proof :

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

    In 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.

    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

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