To determine whether a right triangle with two congruent legs is always a 45-45-90 triangle, let's analyze the properties of such a triangle:
1. Properties of a Right Triangle:
A right triangle has one angle equal to 90 degrees.
2. Congruent Legs:
If both legs of the triangle are congruent, this means that the two legs have the same length. In a right triangle, the legs are the two sides that form the right angle.
3. Angles in a Triangle:
The sum of the angles in any triangle is always 180 degrees. In a right triangle, one of the angles is already 90 degrees. Therefore, the sum of the other two angles must be 90 degrees.
4. Isosceles Right Triangle:
When a right triangle has two congruent legs, it is also known as an isosceles right triangle.
Given that the legs are congruent:
- The two angles opposite the congruent sides must also be congruent.
- Since these two angles add up to 90 degrees, each angle must be 45 degrees.
Thus, a right triangle with two congruent legs indeed has two angles of 45 degrees each, in addition to the 90-degree angle.
Therefore, the right triangle described is always a 45-45-90 triangle.
The correct answer is:
A. True
