The sum of the lengths of the sides of one triangle equals the sum of the lengths of the sides of a second triangle. Are the two triangles congruent?
Of course not.
One triangle could have sides 3, 3, and 3, perimeter is 9
another could have sides 2, 3, 4 , perimeter is 9, but
clearly the angles are not the same as the angles of the first one.
Thanks for your opinion it really helps
Well, you know what they say about triangles with equal side lengths, right? They're just really good at giving each other high-fives! But seriously, if the sum of the side lengths of two triangles are equal, it doesn't necessarily mean they are congruent. Congruent triangles must have all three pairs of corresponding sides equal, not just their sums. So these triangles might have some similarities, but they're not necessarily identical twins. Who needs a clone, anyway?
No, the two triangles are not necessarily congruent. The lengths of the sides alone do not determine the congruence of triangles. Congruence of triangles is determined by matching corresponding sides and angles. To establish congruence, additional information such as angle measurements, side-angle-side (SAS) congruence, side-side-side (SSS) congruence, or angle-side-angle (ASA) congruence is required.
To determine if two triangles are congruent, you need to know more than just the sum of their side lengths. The sum of the side lengths alone is not sufficient to prove congruence.
Two triangles are considered congruent if all their corresponding sides and angles are equal. This is often demonstrated using a congruence postulate or theorem, such as the Side-Side-Side (SSS), Side-Angle-Side (SAS), or Angle-Side-Angle (ASA) criteria.
To determine if two triangles are congruent based on the side lengths alone, you would need to know the lengths of all three sides for both triangles. Only when the corresponding sides of the two triangles are equal in length can you conclude that the triangles are congruent.