Solve for the value of x in the diagram below.
Solve for the value of x in the diagram below.
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
If we increase one side while keeping the other two sides the same size the side that is getting longer will also have the opposite angle get bigger. A triangle that has two sides that are the same length means the opposite angles must also be equal.
We can compare the two sets of sides to see what is the defining difference.
We can see that for any side we look at, the other two side lengths when combined are longer.
For the impossible sides, two of the sides we can choose the other two sides combined are longer. However, looking at the longest side, the two shorter sides combined are still smaller than the longest side. This is the condition which determines whether a triangle is possible or not. For a triangle the combined length of each pair of sides is longer than the remaining side.
Will three sides of length 3,\,5, and 9 make a triangle?
For a triangle to be possible with all three sides, the combined length of each pair of sides is longer than the remaining side.