Question

In the given figure, OD = 2 × OB, OC = 2 × OA and CD = 2 × AB then △ AOB ~ △ COD by ______.

Options

• AA

• SS

• SAS and SSS

• SSS

Answer 1

SSS

Explanation:

Given,

⇒ OD = 2 × OB

⇒ `(OD)/(OB)`​ = 2 .......(1)

⇒ OC = 2 × OA

⇒ `(OC)/(OA​)` = 2 .......(2)

⇒ CD = 2 × AB

⇒ `(CD)/(AB)​` = 2 .......(3)

From equation (1), (2) and (3), we get:

⇒ `(OD)/(OB) = (OC)/(OA​) = (CD)/(AB)`

∴ △ AOB ~ △ COD (By S.S.S. postulate)