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Question

Question 1
If two lines intersect, prove that the vertically opposite angles are equal.

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Solution

Given, two lines AB and CD intersect at point O.
To prove
(i) AOC=BOD
(ii) AOD=BOC
Proof:
(i) Ray OA stands on line CD.
AOC+AOD=180 [linear pair axiom]…(i)
Ray OD stands on line AB.
AOD+BOD=180 [linear pair exiom]…(ii)

From the equations (i) and (ii),
AOC+AOD=AOD+BOD
AOC=BOD
(ii) Ray OD stands on line AB.
AOD+BOD=180 [linear pair axiom]…(iii)
Ray OB stands on line CD.
DOB+BOC=180 …(iv)
From equations (iii) and (iv)
AOD+BOD=DOB+BOC
AOD=BOC
Hence proved.


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