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Prove that: vertically opposite angles are …

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Prove that: vertically opposite angles are equal.

Posted by Anik Das 5 years, 2 months ago

CBSE > Class 09 > Mathematics

2 answers

Yogita Ingle 5 years, 2 months ago

let AB and CD be two lines intersecting at O . 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)

We can write ∠ AOD + ∠ BOD = 180° (Linear pair axiom)……………(2)

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

∠ AOC + ∠ AOD = ∠ AOD + ∠ BOD

This implies that ∠ AOC = ∠ BOD

Therefore it is proved lines intersect each other then the vertically opposite angles are equal.

1Thank You

Muskan Tanwar 5 years, 2 months ago

Yes

2Thank You

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Posted by Yash Pandey 7 months, 1 week ago

CBSE > Class 09 > Mathematics