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.

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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Both the statements are correct

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Both the statements are incorrect

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Solution

The correct option is B 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

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. Which of the following statements are true and which of them are false?

(i) All squares are congruent.
(ii) If two squares have equal areas, they are congruent.
(iii) If two figures have equal areas, they are congruent.
(iv) If two triangles are equal in area, they are congruent.
(v) If two sides and one angle of a triangle are equal to the corresponding two sides and angle of another triangle, the triangle are congruent.
(vi) If two angles and any side of a triangle are equal to the corresponding angles and the side of another triangle then the triangles are congruent.
(vii) If three angles of a triangle are equal to the corresponding angles of another triangle then the triangles are congruent.
(viii) If the hypotenuse and an acute angle of a right triangle are equal to the hypotenuse and the corresponding acute angle of another right triangle then the triangle are congruent.
(ix) If the hypotenuse of a right triangle is equal to the hypotenuse of another right triangle then the triangles are congruent.
(x) If two triangles are congruent then their corresponding sides and their corresponding angles are congruent.

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.

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