Triangle Properties Analysis: Can a 90° Right Triangle Be Equilateral?

Can a right triangle be equilateral?

To solve this problem, we'll follow these steps:

• Step 1: Identify the properties of a right triangle.
• Step 2: Identify the properties of an equilateral triangle.
• Step 3: Compare these properties to determine if a right triangle can be equilateral.

Now, let's work through each step:

Step 1: A right triangle is defined by having one angle equal to $90^\circ$.
Step 2: An equilateral triangle is defined by having all three sides of equal length and all three angles equal to $60^\circ$.
Step 3: Compare the angle measurements: A right triangle cannot have all angles $60^\circ$ because it requires one angle to be $90^\circ$. Likewise, an equilateral triangle cannot have a $90^\circ$ angle, as all its angles must be $60^\circ$.

Therefore, it is impossible for a right triangle to be equilateral, as they fundamentally differ in angle requirements.

The answer to the problem is No.