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ICSE Class X Math 2014 Paper

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In △ABC,∠ABC=∠DAC.AB=8 cm,AC=\triangle ABC, \angle ABC = \angle DAC. AB = 8\ \mathrm{cm}, AC = 4 cm,A D=5 cm4\ \mathrm{cm}, A\ D=5\ \mathrm{cm}.
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Question : 25 of 52
Marks: +1, -0
Prove that △ACD\triangle ACD is similar to △BCA\triangle BCA .
Solution:  
In △ACD\triangle ACD and △BCA\triangle BCA
∠C  =∠C       (common)   \angle C\;=\angle C\;\;\;\text{ (common) }\;
∠ABC  =∠DAC       (given)   \angle ABC\;=\angle DAC\;\;\;\text{ (given) }\;
∴    △ACD  ∼△BCA(AA   postulates)   \therefore\;\;\triangle ACD\;\sim\triangle BCA (\text{AA}\;\text{ postulates) }\;
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