Question

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.

• A. Both the statements 1 and 2 are true
• B. Both the statements 1 and 2 are false
• C. Statement 1 is true and statement 2 is false
• D. Statement 1 is false and statement 2 is true

Answer 1

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 $\Delta ABC$
$=\frac{1}{2}\times BC\times AM$
$=\frac{1}{2}\times 8\times 6c{m}^2$
$=24c{m}^2$
In fig.2, the area of the parallelogram ABCD
$=base\times height$
$=6\times 4c{m}^2$
$=24c{m}^2$
Here, area of $\Delta ABC$ and parallelogram are equal.But, they are not congruent.