Q. 1 4.2( 133 Votes )

State which pairs of triangles in Fig. are similar.Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form:

Answer :

(i) From the figure:

A = P = 60°

B = Q = 80°

C = R = 40°

Therefore, ΔABC ΔPQR [By AAA similarity]

Now corresponding sides of triangles will be propotional,

From the triangle,

Hence the corresponding sides are propotional

Thus the corresponding angles will be equal

The triangles ABC and QRP are similar to each other by SSS similarity

(iii) The given triangles are not similar because the corresponding sides are not proportional

(iv) In triangle MNL and QPR, we have

M = Q = 70o


Therefore, MNL and QPR are not similar.

(v) In triangle ABC and DEF, we have

AB = 2.5, BC = 3

A = 80o

EF = 6

DF = 5

F = 80o


B ≠ F

Hence, triangle ABC and DEF are not similar

(vi) In triangle DEF, we have

D + E + F = 180o (Sum of angles of triangle)

70o + 80o + F = 180o

F = 30o

In PQR, we have

P + Q + R = 180o

P + 80o + 30o = 180o

P = 70o

In triangle DEF and PQR, we have

D = P = 70o

F = Q = 80o

F = R = 30o

Hence, ΔDEF ~ ΔPQR (AAA similarity)

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