Consider the following statements:
Statement 1: All similar triangles are congruent.
Statement 2: All congruent triangles are similar.

Both statements 1 and 2 are correct.

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Both statements 1 and 2 are incorrect.

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Statement 1 is correct but statement 2 is incorrect.

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Statement 1 is incorrect but statement 2 is correct.

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Solution

The correct option is D Statement 1 is incorrect but statement 2 is correct.
Similar triangles have same shape while congruent traingles have same shape and same size.
Hence, all congruents triangles are similar but all similar traingles are not congruent.

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Similar questions

Q. Consider the following statements:
Statement 1: All similar triangles are congruent.
Statement 2: All congruent triangles are similar.

Q. Which of the following is true?
Statement I : All similar triangles are congruent.
Statement II: All congruent triangles are similar.

Q. Three students Pia, Sia and Tia wrote a statement on a blackboard.
Pia wrote, "All rectangles are congruent".
Sia wrote, "All equilateral triangles are congruent".
Tia wrote, "All right angled triangles are congruent".
Who wore the INCORRECT statement?

State, true or false :
(i) Two similar polygons are necessarily congruent.
(ii) Two congruent polygons are necessarily similar.
(iii) All equiangular triangles are similar.
(iv) All isosceles triangles are similar.
(v) Two isosceles-right triangles are similar.
(vi) Two isosceles triangles are similar if an angle of one is congruent to the corresponding angle of the other.
(vii) The diagonals of a trapezium divide each other into proportional segments.

Q. Write the truth value (T/F) of each of the following statements:
(i) Any two similar figures are congruent.
(ii) Any two congruent figures are similar.
(iii) Two polygons are similar if their corresponding sides are proportional.
(iv) Two triangles are similar if their corresponding angles are proportional.

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Consider the following statements: Statement 1: All similar triangles are congruent. Statement 2: All congruent triangles are similar.

The correct option is D Statement 1 is incorrect but statement 2 is correct.Similar triangles have same shape while congruent traingles have same shape and same size. Hence, all congruents triangles are similar but all similar traingles are not congruent.

Consider the following statements:
Statement 1: All similar triangles are congruent.
Statement 2: All congruent triangles are similar.

The correct option is D Statement 1 is incorrect but statement 2 is correct.
Similar triangles have same shape while congruent traingles have same shape and same size.
Hence, all congruents triangles are similar but all similar traingles are not congruent.