State whether the pairs of triangles given in the following figures are congruent or not:

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asked Jun 12 in Class VII Maths by aditya23 (-1,733 points)

State, whether the pairs of triangles given in the following figures are congruent or not:

(vii) △ABC in which AB = 2 cm, BC = 3.5 cm and ∠C = 80°.

And, △ DEF in which DE = 2 cm, DF = 3.5 cm and ∠D = 80°.

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1 Answer

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answered Jun 12 by muskan15 (-3,369 points)

(i) In these triangles, corresponding sides are not equal. Hence these are not congruent triangles.
(ii) In the first A, third angle
= 180°-(40°+ 30°)
= 180° – 70°
= 110°
Now in these two triangles the sides and included angle of the one are equal to the corresponding sides and included angle.
Hence these are congruent triangles
(S.A.S. axiom)
(iii) In these triangles, corresponding two sides are equal but included angles are not-equal. Hence these are not congruent triangles.
(iv) In these triangles, corresponding three sides are equal.
Hence these are congruent triangles.
(S.S.S. Axiom)
(v) In these right triangles, one side and diagonal of the one, are equal to the corresponding side and diagonal are equal. Hence these are congruent triangles. –
(R.H.S. Axiom)
(vi) In these triangles two sides and one angle of the one are equal to the corresponding sides and one angle of the other are equal.
Hence these are congruent triangles.
(S.S. A. Axiom).
(vii) In A ABC. AB = 2 cm, BC = 3.5 cm and ∠C = 80° and in ∆ DEF,
DE = 2 cm, DF = 3.5 cm and ∠D = 80°

From the figure  we see that two corresponding sides  are equal but their included angles are not equal.
Hence, these are not congruent triangles

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