Question

Assertion: If two triangles have the same perimeter, then they are congruent.
Reason: If under a given correspondence, the three sides of one triangle are equal to the three sides of the other triangle, then the two triangles are congruent.
(a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
(b) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
(c) Assertion is correct but Reason is incorrect
(d) Assertion is incorrect but Reason is correct

Answer 1

Hint: If two triangles have the same perimeter, then they are congruent is an incomplete statement that is completed by the reason that says ‘the sides of the two triangles are equal’. Therefore, if two triangles have the same perimeter and all three sides of both of them are equal, then they are congruent.

Complete step-by-step answer:
First of all, we will define what congruent triangles are. Two triangles are congruent if they have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.
The assertion states that “If two triangles have the same perimeter, then they are congruent”. If we consider this statement only, we can see that if two triangles are given which are of the equal perimeter, they may or may not be congruent as the perimeter is the sum of sides of a triangle and the sides can be of any length and can generate the same perimeter. For the triangles having the same perimeter, the areas have to be equal for them to be congruent triangles.
Now, the reason states that if under a given correspondence, the three sides of one triangle are equal to the three sides of the other triangle, then the two triangles are congruent. If all three sides of one triangle are equal to all the three sides of another triangle, their area will be the same. And if the areas are the same, they are congruent triangles.
As you can see here, the reason completes the assertion. Therefore, both assertion and reason are correct and the reason is the correct explanation for the assertion.
Hence, option (a) is the right answer.

Note: Remember the meaning of congruent. A triangle is said to be congruent if any two or all conditions of all the three sides being the same, their perimeters being the same or their areas being the same are fulfilled.