Write whether each pair of triangles are similar.
Problem 1 :
Solution :
AB = 2 and PQ = 4 BC = 3 and QR = 6 CA = 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 = 6 BC = 15 and QR = 10 CA = 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 = 9 BC = 24 and QR = 12 CA = 32 and RP = 16 |
AB/PQ = 27/9 = 3 BC/QR = 24/12 = 2 CA/RP = 32/16 = 2 |
Since the corresponding sides are not same, triangles ∠ABC and ∠PQR not similar.
Problem 4 :
Solution :
AB = 10 and PQ = 30 BC = 9 and QR = 27 CA = 11 and RP = 33 |
AB/PQ = 10/30 = 1/3 BC/QR = 9/27 = 1/3 CA/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 = 5 BC = 16 and QR = 8 CA = 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 = 9 BC = 21 and QR = 18 CA = 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 = 20 BC = 4 and QR = 18 CA = 3 and RP = 16 |
AB/PQ = 5/20 BC/QR = 4/18 CA/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 = 31 BC = 42 and QR = 37 CA = 35 and RP = 26 |
AB/PQ = 39/31 BC/QR = 42/37 CA/RP = 35/26 |
Triangles ABC
and PQR are not similar.
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