Can you draw 2 triangles each having two 45 degree angles and one 90 degree angle that are not similar? justify your answer.?

No, two triangles can be proven similar if all of their angles are equal. If both the triangles are 45-45-90 triangles, they must be similar by definition.

Similar triangles are those of the same shape but different sizes.

So one triangle is defined by c^2 = a^2 + b^2 and the other by C^2 = A^2 + B^2 as both are given as right triangles. As the two non-90 deg angles are both 45 deg, the sides a = b and A = B.

So c^2 = 2a^2 and C^2 = 2A^2. and because the only thing that differs between the two is the size of the sides we can say that A = ka, the larger sides are some multiple of the smaller sides.

So C^2 = 2A^2 = 2 k^2 a^2 = k^2 c^2 and C = kc. Which is to say when the larger sides are some multiple of the smaller sides, so too is the hypotenuse some multiple of the smaller one. In other words the two right triangles are similar as all three sides of the larger triangle are multiples of the smaller one.

So the answer in NO. The two triangles will always be similar. ANS.

no