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Question

# In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form. (i) (ii) (iii) (iv) (v)

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Solution

## (i) ΔABC and ΔPQR∠A=∠Q∠B=∠P∠C=∠RΔABC∼ΔPQR(by AAA similarity) (ii) In ΔABC and ΔEFD∠A=∠D and ABFD=36=12BCED=4.59=12Hence ABFD=BCED=12So ΔABC∼ΔEFD(by SAS similarity) (iii) In ΔABC and ΔPQR∠C=∠Q and CAQR=86=43CBQP=64.5=43Hence CAQR=CBQP=43So ΔABC∼ΔPQR(by SAS similarity) (iv) Finding ratio of sides EDQR=2.55=12EFPQ=24=12DFPR=36=12Hence EDQR=EFPQ=DFPRDFPR=12So ΔDEF∼ΔPQR(SSS similarity) (v) ΔABC and ΔMNRAngle sum=180oIn ΔABC, ∠A+∠B+∠C=180o∠B=180o−(70o+80o)=30oIn ΔMNR, ∠M+∠R+∠N=180o∠R=180o−(30o+80o)=70o∠A=∠M∠B=∠N∠C=∠RΔABC∼ΔMNR(by AAA similarity)

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