In the fig.given, DE ∥ BC such that AE = (\(\frac{1}{4}\))AC. If AB

1.	In the fig.given, DE ∥ BC such that AE = (\(\frac{1}{4}\))AC. If AB = 6 cm, find AD.
Answer» Given: DE∥BC AE = (\(\frac{1}{4}\))AC AB = 6 cm. Required to find: AD. In ΔADE and ΔABC We have, ∠A = ∠A [Common] ∠ADE = ∠ABC [Corresponding angles as AB\|\|QR with PQ as the transversal] ⇒ ΔADE ∼ ΔABC [By AA similarity criteria] Then, \(\frac{AD}{AB}\) = \(\frac{AE}{AC}\) [Corresponding Parts of Similar Triangles are propositional] \(\frac{AD}{6}\)= \(\frac{1}{4}\) 4 x AD = 6 AD =\(\frac{6}{4}\) Therefore, AD = 1.5 cm

In the fig.given, DE ∥ BC such that AE = (\(\frac{1}{4}\))AC. If AB = 6 cm, find AD.

Answer»

Given:

DE∥BC

AE = (\(\frac{1}{4}\))AC

AB = 6 cm.

Required to find: AD.

In ΔADE and ΔABC

We have,

∠A = ∠A [Common]

∠ADE = ∠ABC [Corresponding angles as AB||QR with PQ as the transversal]

⇒ ΔADE ∼ ΔABC [By AA similarity criteria]

Then, \(\frac{AD}{AB}\) = \(\frac{AE}{AC}\) [Corresponding Parts of Similar Triangles are propositional]

\(\frac{AD}{6}\)= \(\frac{1}{4}\)

4 x AD = 6

AD =\(\frac{6}{4}\)

Therefore, AD = 1.5 cm