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Prove that if two lines intersect each other, then vertically opposite angles are equal. |
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Answer» If two lines intersect each other, then the vertically opposite angles are equal. Proof :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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