In Fig. 4.139, = 90° and . If BD = 8 cm and AD = 4 cm, find CD.

We have, <ABC = 90° and BD perpendicular AC

Now, <ABD + <DBC – 90° ………..(I) (<ABC – 90°)

And <C + <DBC – 90° ………..(II) (By angle sum Prop. in ΔBCD) Compare equation I &II

<ABD = <C ………..(III)

In ΔABD and ΔBCD

<ABD = <C (From equation I)

<ADB = <BDC (Each 90°)

Then, ΔABD ~ΔBCD (By AA similarity)

So, (Corresponding parts of similar triangle area proportion)

Or,

Or CD =

Or CD = 16cm