Question

Assertion : If two triangles have the same area, then they are always 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.
(1) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
(2) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
(3) Assertion is correct but Reason is incorrect
(4) Assertion is incorrect but Reason is correct​

Answer 1

Answer: (2)

Step By Step Explanatio: Both assertionand reason are correct but reason is Not the correct explanation for the assertion

hope it helped

Answer 2

Final Answer:

The statement in the Assertion is incorrect but the statement in the Reason is correct​; so the correct option is 4.

Given:

Assertion: If two triangles have the same area, then they are always 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.

To Find:

The correct option from the following is to be found out.

(1) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

(2) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

(3) Assertion is correct but Reason is incorrect

(4) Assertion is incorrect but Reason is correct​

Explanation:

The following points are important for solving the present problem.

• The congruency in the triangles are proved by any of these four rules.

1. SSS congruency or Side-Side-Side congruency
2. SAS congruency or Side-Angle-Side congruency
3. ASA congruency or Angle-Side-Angle congruency
4. RHS congruency or Right (angle)-Hypotenuse-Side congruency

• The congruent triangle have their corresponding sides and angles equal to each other.

Step 1 of 2

The statement in the Assertion is "If two triangles have the same area, then they are always congruent".

This is incorrect because two congruent triangles always have the same area equal to each other, but the reverse is not true.

Any two triangles having the same area, are not always congruent to each other.

Step 2 of 2

Now, the statement in Reason is "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".

This is correct because when the three sides of one triangle are equal to the three sides of the other triangle, then these two triangles become congruent to each other by the SSS congruency.

Therefore, the required correct option is 4, because the Assertion is incorrect but the Reason is correct​.

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