State whether the following statements are true or false. Give reasons for your answer:

(1) If ΔPQR and ΔABC are similar and none of them is equilateral, then all the six correspondences between ΔPQR and ΔABC are similarities.

(2) All congruent triangles are similar.

(3) All similar triangles are congruent.

(4) If the correspondences ABC ↔ BAC is similarity, then AABC is an isosceles triangle.

(5) The correspondence PQR ↔ YZX between ΔPQR and ΔYZX is a similarity. If m∠P = 60, m∠R = 40, then m∠Z = 80.

(1) False

For equilateral triangles, all the six correspondences are similarity. But in triangles other than equilateral, the measures of all the angles are not same.

(2) True

Congruent triangles are equal with respect to size and shape, while for triangles to be similar, it is sufficient that their shapes are same.

(3) False

Similar triangles are equal in shape but not in size. For triangles to be congruent, they must be equal in both, shape as well as size. Hence, all similar triangles are not congruent.

(4) True

For ∆ABC, the correspondence ABC↔BAC is a similarity.

∴ ∠A≅∠B

∴BC≅AC

Hence, two sides of ABC are congruent and therefore ∆ABC is an isosceles triangle.

(5) Given statement is true.