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Question

In a parallelogram ABCD, AB = 10 cm, AD = 6 cm. The bisector of ∠A meets DC in E, AE and BC produced meet at F. Find te length CF.

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Solution



AE is the bisector of A. DAE=BAE =x BAE=AED=x (alternate angles)Since opposite angles in ADE are equal, ADE is an isosceles triangle. AD=DE= 6 cm (sides opposite to equal angles)AB=CD=10 cm CD= DE+ ECEC=CD-DEEC=10-6=4 cmDEA=CEF=x (vertically opposite angle)EAD=EFC=x (alternate angles)Since opposite angles in EFC are equal, EFC is an isosceles triangle. CF=CE= 4 cm (sides opposite to equal angles) CF= 4cm

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