Lines and intersect at

MATHEMATICS · Subjective · CBSE · Mathematics · Lines and Angles · Lines and Angles

Problem

Lines ABAB and CDCD intersect at OO. The following six statements regarding the angles formed are given in a random order: 1. ∠AOC+∠AOD=180∘\angle AOC + \angle AOD = 180^{\circ} 2. ∠AOD+∠DOB=180∘\angle AOD + \angle DOB = 180^{\circ} 3. ∠AOC=∠DOB\angle AOC = \angle DOB 4. Adjacent angles on a straight line sum to 180∘180^{\circ}. 5. Things that are equal to the same thing are equal to one another. 6. Vertically opposite angles are equal. (a) Arrange statements 1–5 in a logical sequence that forms a valid proof of statement 6. (b) Using the correctly ordered statements, write a paragraph proof of the result “Vertically opposite angles are equal,” beginning with the headings Given, To Prove, Proof, and Conclusion. (c) At each logical step, clearly name the axiom or theorem you have used.

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