Is it possible to have a triangle that the sum of the measures of the small and medium sides is equal to the measure of the large side?
To determine whether it is possible to have a triangle where the sum of the measures of the small and medium sides is equal to the measure of the large side, we need to refer to the triangle inequality theorem.
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. In other words, for a triangle with sides a, b, and c, a + b > c, a + c > b, and b + c > a.
So, in this case, let's assume we have a triangle with sides a, b, and c, where a and b are the small and medium sides, and c is the large side. According to the triangle inequality theorem, a + b > c.
Now, if we want to have a triangle where the sum of the measures of the small and medium sides is equal to the measure of the large side, we would need a + b = c.
Since a + b > c is a necessary condition for a triangle to exist, and a + b = c is not satisfied here, it means that it is not possible to have a triangle with the sum of the measures of the small and medium sides equal to the measure of the large side.