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-A- Both the statements are correctB- Statement 1 is incorrect and statement 2 is correctC- Statement 1 is correct but statement 2 is incorrectD- Both the statements are incorrect

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Introduction

Statement 1 :...

Question

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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Statement 1 is correct but statement 2 is incorrect

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Statement 1 is incorrect and statement 2 is 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.

Suggest Corrections

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.

Q. Let

P (n) = 1 + 3 + 5 + . . . . + (2 n - 1) = 3 + n^{2}, n \in N

Statement

1

: The statement

P (n)

is true
Statement

2

: According to the principle of mathematical induction, if

P (k) \Rightarrow P (k + 1)

is true, then the given statement

P (n)

is true

Q. Consider the following statements:
1. If two triangles are equiangular, then they are similar.
2. If two triangles have equal area, then they are similar.
Which of the statements given above is/are correct?

Statement 1: Area of a rectangle with length ‘l’ and breadth ‘b’ is equal to ‘l $\times$ b’.

Statement 2: All squares are rectangles with l = b

Pick the correct option from the following

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