Q. 214.5( 6 Votes )

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Answer :

Given: CA – CB


AP x BQ = AC2


To prove: ΔAPC ~ BCQ


Theorem Used:


If two corresponding sides and one angle of two triangles are equal, the triangles are said to be similar.


Proof:


AP X BQ = AC2 (Given)


AP x BC = AC x AC


As AC = BC


AP x BC = AC x BC


…… (i)


Since, CA = CB (Given)


Then, CAB = CBA (Opposite angle to equal sides) …. (ii)


Now, CAB +CAP = 180° (Linear pair of angles) …… (iii)


And CBA + CBQ = 180° (Linear pair of angles) ……. (iv)


Compare equation (ii) (iii) & (iv)


CAP = CBQ …… (v)


In ΔAPC and ΔBCQ


CAP = CBQ (From equation v)


(From equation i)


Then, ΔAPC ~ ΔBCQ (By SAS similarity)


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