which triangle congruence theorem explains why all triangles are rigid? is it SSS, SAS, ASA, or AAS?
The triangle congruence theorem that explains why all triangles are rigid is the Side-Side-Side (SSS) congruence theorem.
To understand why, it is important to first understand what triangle congruence means. Two triangles are considered congruent if all corresponding sides and angles have the same measures. In other words, they are the same size and shape.
The SSS congruence theorem states that if the three sides of one triangle are congruent to the corresponding three sides of another triangle, then the two triangles are congruent. This means that if we know that all three sides of a triangle are congruent to the corresponding sides of another triangle, we can conclude that the two triangles are identical in shape and size.
Why does this theorem show that all triangles are rigid? The reason is that if we start with one triangle and fix the lengths of its three sides, the angles of the triangle will also be fixed. In other words, there is a one-to-one correspondence between side lengths and angles in a triangle.
Now, if we try to change the lengths of any side of our original triangle while keeping the other two sides fixed, the triangle would no longer satisfy the SSS congruence theorem. This means that we cannot change the size and shape of the triangle while keeping all three sides congruent. Therefore, the SSS congruence theorem shows that all triangles are rigid.
To summarize, the triangle congruence theorem that explains why all triangles are rigid is the Side-Side-Side (SSS) congruence theorem. If the three sides of one triangle are congruent to the corresponding three sides of another triangle, then the two triangles are congruent, making triangles unable to change in size and shape while keeping all three sides congruent.