One of the basic question from similarity chapter in which angle of a triangle is similar to another angle of a triangle We need to

(i)Prove that ΔABC and ΔAED are similar

(ii) Find the length of AC

Book- ML Aggarwal, Avichal Publication, Similarity, chapter 13, question no 10b

## From the given figure,

(i) ∠A=∠A (common angle for both triangles)

∠ACB=∠ADE [given]

Therefore, △ABC∼△AED

(ii) from (i) proved that, △ABC∼△AED

So, BC/DE=AB/AE=AC/AD

AD=AB−BD

=6–1=5

Consider, AB/AE=AC/AD

6/3=AC/5

AC=(6×5)/3

AC=30/3

AC=10cm.