Question

State the SSS congruence rule of triangles

Answer 1

Hint: Before answering the question, first explain what congruence is and then how the two triangles can be proved that they are congruent by SSS or Side – Side – Side axiom of congruency. Also, what conditions should be necessary to prove that two triangles are congruent using SSS axiom of congruency.

Complete step by step answer:
In the question, we have been asked to state the SSS congruence rule of triangles. Before that, we will see what congruence is. In geometry, two figures or objects are congruent if they have the same shape and size as the mirror image of the other. More formally, two sets of the points are congruent if and only if one can be transferred to the other is an isometry, which is a combination of the rigid motions, normally translation, rotation, and reflection. This means that either the object can be repositioned and reflected (but not resized) to coincide precisely with the other object. So, two distinct plane figures on a piece of paper are congruent if we cut them out and match them completely.
In elementary geometry, the word congruent is often used. The word equal is often used in place of congruent for these objects.
- Two line segments are congruent if they have the same length
- Two angles are congruent if they have the same measure.
- Two circles are congruent if they have the same radius.
In this way, two plane figures are congruent implies that their corresponding characteristics are congruent or equal including not just their opposite sides and angles, but also their corresponding diagonals, perimeters, and areas.
When we have to prove two triangles congruent, we generally use some axioms to prove it. One of them is the Side – Side – Side (SSS) axiom of congruency.
Side – Side – Side (SSS): This states that if three sides of a triangle are congruent to three sides of another triangle, the triangles are congruent.


Note:
Generally it is said that if two triangles are congruent then we can say that they are similar to each other so all the conditions for which two triangles are congruent can also be taken as conditions for similarity too.