Question
The parallel sides of a Trapezium is 20 and 46cm
respectively and the non-parallel sides were 10 cm and 24 cm respectively. If the non-parallel sides were extended and the meet each other at m. find the value of ∠m?Solution
Let ABCD be the trapezium with AB ∥ CD The non-parallel lines AD and BC were extended and they meet each other at point m… Now construct a line CE parallel to DA. AD = CE = 10cm, AE = CD = 20cm BE = (46-20) = 26cm Now, CE=10cm, BC=24cm and BE=26cm BE² = CE² + BC² Therefore Triangle BCE is a right angled triangle with ∠BCE = 90⁰ ∠m = ∠BCE = 90⁰ (Corresponding Angles are equal)
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