Question

How many triangles can be constructed with sides measuring \[1\] m, \[2\]m and \[2\]m \[?\]

Answer 1

Hint: For solving above problem we must know the triangle congruence theorem. How a triangle will be different from another triangle in respect of sides and angles can only understand by congruence theorem. Therefore, first, we are seeing different congruence theorems and then based on theorems try to find out how many triangles are possible from above-given sides.

Complete step by step answer:
First, writing triangle congruence theorems,
Side Side Side (SSS)
Side Angle Side (SAS)
Angle Side Angle (ASA)
Writing statements of above triangle congruence theorems,
Side Side Side (SSS)
It says triangles are congruent if three sides of one triangle are equal to the corresponding sides of the other triangle.
Side Angle Side (SAS)
It says triangles are congruent if any pair of corresponding sides and their included angle are equal.
Angle Side Angle (ASA)
It says triangles are congruent if any two angles and their included side are equal.
In the given problem three sides of the triangle are given. So, it is related to the Side, Side, Side congruence theorem.
Now by the above-given statement of Side, Side, Side congruence theorem, it is understood that when all the three sides of the triangles are given and we have to construct the triangle then we can only construct one triangle because if we try to construct another triangle by using same sides of the triangle it becomes congruent to the first triangle.

Hence, only one triangle can be constructed with sides measuring \[1\] m, \[2\]m and \[2\]m.

Note: From the above-given sides of the triangle it is also concluded that it is an example of the Isosceles triangle because two sides are equal among given three sides.