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

Question

Britney Hood · Accepted Answer

Theorems for congruency can be used to reach a conclusion.
The first is the SSS theorem, which states that two triangles are congruent if their three sides are equal to those of another triangle. As a result, whenever three sides are given, a distinct triangle can always be found. 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.
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.
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^{\circ}

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

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

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