Q1 of 62 Page 186

Find the unknown values in each of the following figures. All lengths are given in centimeters. (All measures are not in scale)

To find x and y i.e. AF and GD respectively.

Now,


In ΔFBC and ΔGBD


∠FBC = ∠GBD (common)


∠BFC = ∠BGD by corresponding angles (DE∥CF)


∴ ΔFBC ∼ ΔGBD


(∵ ΔFBC ∼ ΔGBD)



⇒ y = 2.5 cm


EF = DC (∵ EFCD is a parallelogram)


⇒ EF = 7 cm


Now,


In ΔAEF and ΔABC


∠AEF = ∠ABC by corresponding angles (EF∥BC)


∠AFE = ∠ACB by corresponding angles (EF∥BC)


∴ ΔAEF ∼ ΔABC


(∵ ΔAEF ∼ ΔABC)



⇒ x = 8.4 cm


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