Lines and intersect at point

MATHEMATICS · Multi-part · CBSE · Mathematics · Lines and Angles · Lines and Angles

Problem

Lines l1l_{1} and l2l_{2} intersect at point OO. A partially completed proof is given to establish that the vertically opposite angles thus formed are equal. Step 1 ∠AOC+∠COD=180∘\angle AOC + \angle COD = 180^{\circ} (Reason ____) Step 2 ∠COD+∠DOB=180∘\angle COD + \angle DOB = 180^{\circ} (Reason ____) Step 3 ∠AOC+∠COD=∠COD+∠DOB\angle AOC + \angle COD = \angle COD + \angle DOB (Reason ____) Step 4 ∠AOC=∠DOB\angle AOC = \angle DOB (Reason ____) Step 5 Similarly, ∠AOD=∠COB\angle AOD = \angle COB. Answer the following: (i) Fill in the missing reasons for Steps 1–4, choosing from: linear pair axiom, subtraction property of equality, common notion “Things equal to the same thing are equal to one another.” (ii) After completing the reasons, rewrite the entire argument in paragraph form with proper structure and a clear concluding statement. (iii) Name the pairs of equal angles that have been proved and explain briefly why they are called ‘vertically opposite’.

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