In the given figure , AB || CD || EF given AB = 7.5 cm , DC =y cm , EF = 4.5 cm , BC = x cm . Calculate the values of x and y. .
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∆CDC ∼ ∆ABE
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Similarly ∆BDC ∼ ∆BEF
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Answer:
• In △BCD and △BEF :
↠ ∠DBC = ∠FBE (Common angle)
↠ ∠BCD = ∠BEF (Corresponding angles of parallel lines CD and EF)
↠ ∠BDC = ∠BFE (Corresponding angles of parallel lines CD and EF)
∴ △BCD ∼△BEF (AAA rule)
Hence,
⇒ BE/BE = BF/BD = EF/CD (Corresponding sides)
⇒ x+3/x = BF/BD = 4.5/y ..(I)
Similarly, △FCD ∼△FAB
∴ y = 16/45 cm and, x = 5 cm
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