+29 lf the sum of one of the base angIes and the vertex angIe is the same for two different isosceIes triangIes, must the triangIes be simiIar?
+129899 Mmmm....this is an interesting question
Let the base angles of both triangles be equal
And let's assume that we can create similar triangles
Let the base angle in one triangle = x and the apex angle = y
Their sum is x + y
Now let the base angle of another triangle = (x - a) and let the apex angle = (y + a) where a is positive
Their sum is also x + y
In the first triangle 2x + y =180
In the second triangle
2 ( x - a) + ( y + a ) =180 simplify
2x + y - a = 180
2x + y = 180 + a
Since a is positive....2x + y in one case =180 and in the other case it is more than 180
This is impossible.....so.....since the final result leads to an absurdity.....our assumption must be false....
So....the triangles cannot be made similar by having the same sums for one base angle and the apex angle
