# DETERMINE WHETHER THE TRIANGLES ARE SIMILAR

Write whether each pair of triangles are similar.

Problem 1 : Solution :

 AB = 2 and PQ = 4BC = 3 and QR = 6CA = 4 and RP = 8 AB/PQ = 2/4 = 1/2 ---(1)BC/QR = 3/6 = 1/2 ---(2)CA/RP = 4/8 = 1/2 ---(3)

(1) = (2) = (3)

AB/PQ = BC/QR = CA/RP = 1/2

By using Side – Side – Side theorem,

Since corresponding the sides are in the same ratio, triangles ABC and PQR similar.

Problem 2 : Solution :

 AB = 9 and PQ = 6BC = 15 and QR = 10CA = 18 and RP = 12 AB/PQ = 9/6 = 3/2 ----(1)BC/QR = 15/10 = 3/2 ----(2)CA/RP = 18/12 = 3/2 ----(3)

AB/PQ = BC/QR = CA/RP = 3/2

Since, corresponding the sides are in the same ratio.

So, ABC and PQR similar.

Problem 3 : Solution :

 AB = 27 and PQ = 9BC = 24 and QR = 12CA = 32 and RP = 16 AB/PQ = 27/9 = 3BC/QR = 24/12 = 2CA/RP = 32/16 = 2

Since the corresponding sides are not same, triangles ABC and PQR not similar.

Problem 4 : Solution :

 AB = 10 and PQ = 30BC = 9 and QR = 27CA = 11 and RP = 33 AB/PQ = 10/30 = 1/3BC/QR = 9/27 = 1/3CA/RP = 11/33 = 1/3

AB/PQ = BC/QR = CA/RP = 1/3

Since the corresponding the sides are in the same ratio triangles ABC and PQR are similar.

Problem 5 : Solution :

 AB = 10 and PQ = 5BC = 16 and QR = 8CA = 12 and RP = 6 AB/PQ = 10/5 = 2 ---(1)BC/QR = 16/8 = 2 ---(2)CA/RP = 12/6 = 2 ---(3)

AB/PQ = BC/QR = CA/RP = 2

Since, corresponding the sides are in the same ratio.

So, ABC and PQR similar.

Problem 6 : Solution :

 AB = 18 and PQ = 9BC = 21 and QR = 18CA = 21 and RP = 18 AB/PQ = 18/9 ---(1)BC/QR = 21/18 ---(2)CA/RP = 21/18 ---(3)

Since corresponding the sides are not in the same ratio, triangles ABC and PQR not similar.

Problem 7 : Solution :

 AB = 5 and PQ = 20BC = 4 and QR = 18CA = 3 and RP = 16 AB/PQ = 5/20BC/QR = 4/18CA/RP = 3/16

Since corresponding the sides are not in the same ratio, triangles ABC and PQR not similar.

Problem 8 : Solution :

 AB = 39 and PQ = 31BC = 42 and QR = 37CA = 35 and RP = 26 AB/PQ = 39/31BC/QR = 42/37CA/RP = 35/26

Triangles ABC and PQR are not similar.

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