prove that area of two similar triangle is equal to the ratio oftheir

1.	prove that area of two similar triangle is equal to the ratio oftheir corresponding side
Answer» Areas of Similar Triangles NCERT Solutions Grade 10 Given: △ABC ~ △DEF. AP is the median to side BC of △ABC and DQ is the median to side EF of △DEF.ACDF=BCEF {Corresponding sides of similar triangles are proportional}⇒ACDF=2PC2QF=PCQF (1){P is the mid-point of BC and Q is the mid-point of EF} To Prove: ar(△ABC)ar(△DEF)=AP2DQ2 Proof: ar(△ABC)ar(△DEF)=BC2EF2{The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides}⇒ar(△ABC)ar(△DEF)=(2PC)2(2QF)2=PC2QF2 (2) In △APC and △DQFACDF=PCQF from (1)And, ∠C=∠F {Corresponding angles of similar triangles are equal} Therefore, by SAS similarity criterion, △APC ~ △DQFTherefore, APDQ=PCQF (3) Putting (3) in (2), we getar(△ABC)ar(△DEF)=AP2DQ2 Hence Proved

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