Prove that the ratio of correspondi...
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Prove that the ratio of corresponding sides of two similar triangles is the same as the ratio of their corresponding angle bisectors. 1 given fiure

IIT/JEE
Maths
Solution
164
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given that ( Delta A B C sim D P Q R ) ( angle B A C=angle Q P R ) ( angle A B C=angle P Q R ) Now AD is angle bisec tor of bitesc ( angle B A C ) PS in angle Gisector of ( angle ) PQR Now in ( triangle A B D ) & ( Delta P Q S ) ( angle B A D=angle Q P S[because text { as } angle B A C=angle Q P R] ) ( angle A B D=angle P Q S[because angle A B C=angle P G B] ) ( B y ) A A similarity criteria ( therefore quad frac{A B}{P Q}=frac{A D}{P S} ) Lence proved
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