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

Both I and II

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Only statement I

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Only statement II

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Both statements are false

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Solution

The correct option is C Only statement II
In congruent triangles, all the corresponding sides and corresponding angles are equal whereas in similar triangles only the corresponding angles are equal and ratio of corresponding sides is the same.
So, for similar triangles to be congruent the ratio of corresponding sides must be 1. But all congruent triangles are always similar.
Hence only statement II is correct.

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Similar questions

Q. Which of the following statements are true and which are false;
(i) All squares are congruent.
(ii) If two squares have equal areas, they are congruent.
(iii) If two rectangles have equal area, they are congruent.
(iv) If two triangles are equal in area, they are congruent.

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

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

Q. In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

A: If ∆ABC and ∆PQR are congruent triangles, then they are also similar triangles.

R: All congruent triangles are similar but the similar triangles need not be congruent.

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

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