Lines and intersect at

MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

Lines ABAB and CDCD intersect at OO. Ray OEOE bisects ∠AOC\angle AOC and ray OFOF bisects ∠BOD\angle BOD (the vertically opposite angle to ∠AOC\angle AOC). Prove the following statements. (i) Express ∠EOF\angle EOF in terms of ∠AOC\angle AOC. (ii) Express ∠FOE\angle FOE in terms of ∠BOD\angle BOD. (iii) Using the results of parts (i) and (ii) together with the fact that ∠AOC=∠BOD\angle AOC = \angle BOD, prove that ∠EOF=∠FOE\angle EOF = \angle FOE.

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