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.