In the given figure, ABC is a triangle with ∠EDB = ∠ACB. Prove that △ABC ~ △EBD. If BE = 6 cm, EC = 4 cm, BD = 5 cm and area of △BED = 9 cm². Calculate the :

(i) length of AB

(ii) area of △ABC

In the given figure, ABC is a right angled triangle with ∠BAC = 90°.

(i) Prove that : △ADB ~ △CDA.

(ii) If BD = 18 cm and CD = 8 cm, find AD.

(iii) Find the ratio of the area of △ADB is to area of △CDA.

ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that :

(i) △ADE ~ △ACB

(ii) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.

(iii) Find, area of △ADE : area of quadrilateral BCED.