Prove that \triangle A C D is similar to \triangle B C A .

ICSE Class X Math 2014 Solved Paper - Question 25

In $△ A B C, ∠ A B C=∠ D A C . A B=8 {\cm}, A C=$ $4 {\cm}, A D=5 {\cm}$ .

Question : 25 of 52

Marks: +1, -0

Prove that

△ A C D

is similar to

△ B C A

Solution:

△ {\ACD}

and

△ {\BCA}

∠ {\C}\;=∠ {\C} \;\; \;\text " (common) "\;

∠ {\ABC}\;=∠ {\DAC} \;\; \;\text " (given) "\;

∴ \;\; △ {\ACD}\;∼ ∆ {\BCA}( {\AA} \;\text " postulates) "\;

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