Question

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

Answer 1

Onle one triangle.

Explanation:

One can draw a conclusion based on theorems for congruency.

1. First is `SSS` theorem which says that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent. Therefore, when three sides are given, we an always find a unique triangle. But note that for a triangle to form, the sum of smaller two sides should be greater than the third (largest) side. Here as two larger sides are equal, this automatically follows.

2. The other is `SAS` i.e. when two sides and included angle is given. However, if two sides are given but angle given is not the included angle, then we may have none, one or two triangles. This will depend upon the size of the sides and the given angle.

3. `ASA` i.e. when a side and any two angles are given, only one triangle can be formed. This is as if two angles are equal, third will always be equal as their sum is always `180^@`.

4. `RHS` i.e. when in a right angle, hypotenuse and one side is given.