Q17 of 56 Page 6

In fig., we have AB∥CD∥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.

Given: AB = 6cm


CD = x cm


EF = 10 cm


BD = 4cm


DE = y cm


To find: The value of x and y.


Theorem Used:


If two corresponding angles of two triangles are equal the triangles are said to be similar.


Explanation:



Consider ΔADB and ΔEDF,
∠ADB = ∠EDF (Vertical angles)
∠ABD = ∠FED (Alternate angles)
∠BAD = ∠EFD (Alternate angles)
∴ ΔADB ~ ΔEDF (AAA criterion)

⇒ 6y = 40
⇒ y = 6.67
Similarly, ΔADE ~ ΔCDE (AA criterion)






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


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