$proof of isosceles triangle theorem$

Arrange the three straws in the form of a triangle, such that the side AB is represented by red straw, side BC by blue straw, and side AC by green straw. Let the red straw measure 4 cm and the blue straw 10 cm, while the length of the green straw is unknown. Let their colors be red, blue and green in color. Take three straws of different lengths and colors. Let us do a simple activity to use the above theorem. Thus, the third side could have any value between 5 and 13. Let the length of the third side be x units.ĭifference of two sides < unknown side < sum of the two sides The inequality theorem is applicable to all types of triangles such as scalene, isosceles, and equilateral. Thus, they don’t satisfy the triangle inequality theorem. This proves that we cannot make a triangle with these three line segments. In contrast, if we consider the line segments of lengths 6, 8, and 17 units, we find that the line segment measuring 17 units is longer than the length of the other two line segments combined. Here, we see that none of the line segments are longer that the sum of the other two line segments. This is because those line segments satisfy the triangle inequality theorem. We could make a triangle with line segments having lengths 6, 8, and 10 units.

It tells us that for 3 line segments to form a triangle, it is always true that none of the 3 line segments is greater than the lengths of the other two line segments combined. The above theorem describes the relationship between the three sides of a triangle.

Proof of isosceles triangle theorem