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.

Both the statements 1 and 2 are true

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Both the statements 1 and 2 are false

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Statement 1 is true and statement 2 is false

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Statement 1 is false and statement 2 is true

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Solution

The correct option is C Statement 1 is true and statement 2 is false
Let us consider the following two shapes-

In fig.1, the area of the $Δ A B C$
$= \frac{1}{2} \times B C \times A M$
$= \frac{1}{2} \times 8 \times 6 c m^{2}$
$= 24 c m^{2}$
In fig.2, the area of the parallelogram ABCD
$= b a s e \times h e i g h t$
$= 6 \times 4 c m^{2}$
$= 24 c m^{2}$
Here, area of $Δ A B C$ and parallelogram are equal.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 two statements:

Statement 1: If two line segments have the same length, then they are congruent.
Statement 2: If two line segments are congruent, then they have the same length.

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.

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.

Question 92

State whether the statement is True or False.

Two figures are congruent if they have the same shape.

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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.

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.