In Fig. 7.146, we have AB ||CE||EF. If AB=6 cm, CD=x cm, EF= 10 cm, BD=4 cm and DE - y cm, calculate the values of x and y.

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Solution

Consider ΔADB and ΔEDF,

∠ADB = ∠EDF (Vertical angles)
∠ABD = ∠FED (Alternate angles)
∠BAD = ∠EFD (Alternate angles)

∴ ΔADB ~ ΔEDF (ASA criterion)

⇒ BD/DE = AB/FE
⇒ 4/y = 6/10
⇒ 6y = 40
⇒ y = 40/6 = 20/3
⇒ y = 6.67

Similarly, ΔADE ~ ΔCDE (AA criterion)
⇒ DE/BE = DC/BA

⇒ 6.67 / 10.67 = x / 6

⇒ x = 6 x (6.67 / 10.67)

⇒ x = 3.75

hence, the values of x and y are 3.75 and 6.67.

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