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.

Answer

(i) `Delta ABC~ Delta QPR` (AAA- similarity)
(ii) not similar
(ii) `Delta CAB~ Delta QRP` (SAS- similarity)
`(iv) Delta EFD~ Delta PQR` (SSS-similarity)
`(v) Delta ABC~ Delta MNR` (AA-similarity)

Explanation

`(i) angle A= angleQ, angle B= angle P and angle C= angle R`.
`:. Delta ABC~Delta PQR` (AAA-similarity)
(ii) SAS-similarity is not satisfied as included angles are not equal.
(iii) `Delta CAB~ Delta PQR` (SAS-similarity) as, `(CA)/(QR)=(CB)/(QP) and angle C= angle Q`.
(iv) `FE=2 cm, FE=3 d, EF=2.5 cm, ,PQ= 4cm, PR = 6 cm,Qr= 5 cm`.
`:. Delta FED~ Delta PQR` (SSS- similarity)
(v) `angle =180^(@)-(angle A+angleC)=180^(@)-(80^(@)+70^(@))=30^(@)`
`:. angle A = angle M and angle B= angle N, and so Delta ABC~ Delta MNR` (AA-similarity)