In fig. 4.144, 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.
We have AB||CD. If AB = 6cm, CD = xcm, EF = 10 cm, BD = 4cm and DE = ycm
In ΔECD and ΔEAB
<ECD = <EAB (Corresponding angles)
Then, ΔECD ~ ΔEAB ………(i) (By AA similarity)
SO, (Corresponding parts of similar triangle are proportion)
Or ………………(ii)
In ΔACD and ΔAEF
<CAD = <EAF (Common)
<ACD = <AEF (Corresponding angles)
Then, ΔACD ~ ΔAEF (By AA similarity)
SO,
Or, …………………….. (iii)
Adding equation iii & ii
So,
Or,
Or, 1 =
Or, x =
Or, x = 3.75cm
From (i) =
Or, =
Or, 6y = 3.75y +15
Or, 2.25y = 15
Or, y =
Or, y = 6.67cm