Statement 1: If two figures A and B are congruent, then they must have equal area.

Statement 2: If two figures A and B have equal area, then they must be congruent.

Both the statements are correct

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Both the statements are incorrect

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Statement 1 is incorrect and statement 2 is correct

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Statement 1 is correct but statement 2 is incorrect

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Solution

The correct option is D Statement 1 is correct but statement 2 is incorrect
Two figures are said to be congruent if they have same shape and size. So, if two figures are congruent, they must have equal areas.

In the above figure, $Δ A B C$ and $Δ D E F$ are congruent. Hence, area of $Δ A B C =$ area of $Δ D E F$

However, the converse is not true.

The square and rectangle shown above have the same area. But they are not congruent.

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Similar questions

Statement 1: If two figures A and B are congruent, then they must have equal area.

Statement 2: If two figures A and B have equal area, then they must be congruent.

Consider the following two statements:
Statement - 1: If two figures have same shape and same size then they are called congruent.
Statement - 2: If two figures have equal area they are called congruent.
Now, choose the correct option.

If two figures have same area, they must be congruent.

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.

Q. If two rectangles have equal area, then they are congruent.

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