A triangle can be drawn if ______ sides given.a)3b)1c)2d)none of these...
Introduction:
A triangle is a closed figure with three sides. To draw a triangle, we need to have information about the lengths of its sides. In this question, we are asked to determine the minimum number of sides required to draw a triangle.
Explanation:
In order to draw a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Triangle Inequality Theorem:
According to the triangle inequality theorem, for any triangle with sides of lengths a, b, and c:
a + b > c
b + c > a
c + a > b
Options:
Let's analyze each option to determine if a triangle can be drawn with that number of sides:
a) 3 sides: If we have the lengths of all three sides, we can apply the triangle inequality theorem to check if a triangle can be drawn. Since all three conditions of the triangle inequality theorem are met, we can draw a triangle with the given side lengths.
b) 1 side: If we have only one side length, we cannot determine a triangle. We need at least two more side lengths to apply the triangle inequality theorem.
c) 2 sides: If we have the lengths of two sides, we can apply the triangle inequality theorem to check if a triangle can be drawn. In this case, we can determine a triangle by ensuring that the sum of the lengths of the two sides is greater than the length of the third side.
d) None of these: This option implies that no information about the sides is given. Without any side lengths, we cannot determine if a triangle can be drawn.
Conclusion:
Based on the analysis, we can conclude that a triangle can be drawn if we have the lengths of all three sides (option a).
A triangle can be drawn if ______ sides given.a)3b)1c)2d)none of these...
A triangle can be drawn if 3 sides given.,
so the correct answer is 'A'.