Question

Statement 1: Two congruent triangles have equal areas.

Statement 2: Any two triangles with equal areas are always congruent.

Pick the correct option:

• A. Only statement 1 is true
• B. Only statement 2 is true
• C. Both statement 1 and 2 are true
• D. Both statement 1 and 2 are false

Answer 1

The correct option is A

Only statement 1 is true

Statment 1: Two congruent triangles have equal areas.
Two congruent triangles have equal areas since the lengths of their corresponding sides are equal.
So, statment 1 is correct.

Statment 2: Any two triangles with equal areas are always congruent.
Two triangles can have the same area but the lengths of their sides can vary and hence they cannot be congruent.
So, statement 2 is incorrect.