Which of the following statements is sufficient to conclude that two triangles are congruent?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. These have two equal sides and the same perimeter.
SSS (Side-Side-Side): If the three sides of one triangle are equal to the three sides of another triangle, the triangles are congruent.
SAS (Side-Angle-Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
ASA (Angle-Side-Angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, the triangles are congruent.
So from option 1, if 2 sides and perimeter are equal then the third side will also be equal.
So, statement 1 is sufficient to conclude that two triangles are congruent.