Try to construct triangles using match sticks some are shown here can you make a triangle with

a) 3 matchsticks    b) 4 matchsticks    c) 5 matchsticks    d) 6 matchsticks

A triangle is defined as a closed figure made with 3 line segments that form the shape of a triangle.

Answer: We can make triangles with 3, 5, and 6 match sticks.

We will use the triangle inequality theorem to answer this question.  

Explanation:

Look at the below image of how to construct triangles with match sticks.

3 match sticks: One match stick makes one side. So all sides are equal. This will form an equilateral triangle.

4 match sticks: The sum of two sides should be greater than the third side, that is,1 + 1 > 2. Triangle is not possible

5 match sticks: Two sides are equal. The sum of the two sides should be greater than the third side, that is, 2 + 2 > 1. This will form an isosceles triangle.

6 match sticks: All sides are equal. This will form an equilateral triangle.

Therefore, we can make triangles with 3, 5, and 6 match sticks.