1. When the triangle is isosceles, the three points are collinear, i.e. a straight line passes through the three points.
In the case of an equilateral triangle, all three points coincide at the centroid of the triangle.
2. Use Pythagoras theorem, which states that the square of the hypothenuse (the longest side) of a right-triangle is equal to the sum of the squares of the remaining sides.
Therefore the triangle 3,4,5 is a right-triangle.
Thank you for the help. When you gave the example of question 2 is that I need to put for explaining my answer?
Yes, explanations similar to the example would suffice.
However, you need to check in a similar way each of the triplets given in the question.
You will notice that there is one of the four triplets is not Pythagorean.
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