Question

State true or false:
Two circles are always congruent. A) True B) False

Answer 1

Hint: To solve this question we need to know the concept of congruence. The two figures are called congruent if the shape and size of the two figures are the same. For the figure, circle the congruence can be proved by checking the radius of the circle. To check the correctness of the statement we will analyse the circle.

Complete step-by-step solution:
The question asks us to check whether the two circles are always congruent or not. To check the congruency of the circle we need to see whether the circle are of the same shape and size or not so the congruency of the circle depends upon the size of the radius. If the two given circles have the same radius the circumference hence are the same as the circumference is equal to $2\pi r$, where $r$ is the radius of the circle. This means the size of the circle is equal only when the radius of the circle is equal.
Hence don't have the same size always which means the statement given above is false which says all the circles are congruent. The image below shows that the circles are not always congruent. Here f and g are the radius having different values.

$\therefore$ For the statement two circles are always congruent, it is false.

Note: Another approach to the above statement. All circles have the same shape which means they are round. We know that congruent means the same shape but different size. Different circles may have the same or different sizes. All circles are always similar but not congruent.