In Fig, DE∥BC such that AE = (1/4) AC. If AB = 6 cm, find AD.

Given: AE = (1/4) AC

AB = 6 cm

To find: The length of AD.

Theorem Used:

If two triangles are similar, then the ratio of their corresponding sides are equal.

Explanation:

We have, DE||BC, AB = 6cm and AE = 1/4 AC

In ΔADE and ΔABC

∠A = ∠A (Common)

∠ADE = ∠ABC (Corresponding angles)

Then, ΔADE ~ ΔABC (By AA similarity)

So, (Corresponding parts of similar triangle area proportion)

Or (AE = 1/4 AC Given)

Or,

Or, AD = 6/4

Or, AD = 1.5cm