Let's analyze the question step-by-step.
A triangle with two congruent sides is known as an isosceles triangle. An isosceles triangle has two sides of equal length and, consequently, two angles opposite those sides that are also equal.
A 45-45-90 triangle is a specific type of isosceles right triangle where each of the congruent angles measures 45 degrees, and the hypotenuse is √2 times the length of each leg.
Let's consider other cases of isosceles triangles:
1. An isosceles right triangle with angles of 45 degrees.
2. An isosceles triangle that is not a right triangle, for example, an isosceles triangle with angles of 70-70-40 degrees.
Clearly, not all isosceles triangles are 45-45-90 triangles.
So, the claim that a triangle with two congruent sides is always a 45-45-90 triangle is incorrect.
Therefore, the correct answer is:
B. False
