Question

Is triangle ABC congruent to triangle ACB $\left( {\vartriangle ABC \cong \vartriangle ACB} \right)$ ?

Answer 1

Hint: To a triangle to be congruent to another triangle, it should have two equal sides and one equal included angle or two equal angles and one equal included side or three equal sides. If the given triangles satisfy any of these properties then the triangles are congruent.

Complete step-by-step answer:
We are given triangles ABC and ACB.

And we have to find whether these triangles are congruent or not.
Here the vertices B, C of the triangle ABC are swapped in the triangle ACB.
In general, let us consider triangle ABC has 3 different angles and sides.
This means, $AB \ne BC \ne AC,\angle a \ne \angle b \ne \angle c$
So, by comparing the two triangles we have only one similar angle (a) and only one similar side BC=CB.
For two triangles to be congruent, triangles should have at least 2 equal sides and one equal angle or two equal angles and one equal side.
Here there is only one equal angle and only one equal side in both the triangles.
Therefore, triangle ABC is not congruent to triangle ACB.

Note: If the triangle ABC is an isosceles triangle, then AB=AC; then the triangle ACB will also be an isosceles triangle and have AC=AB. So, now there will be one equal angle and two included equal sides for both the triangles which makes the triangles congruent. If the triangle is an isosceles triangle, then ABC is congruent to ACB. This means that it is not necessary that the triangle be congruent to each other if the sides are inverted the other way round.