1. What is a Triangle with 3 90 Degree Angles?

Definition: This calculator demonstrates why a triangle cannot have three 90° angles based on Euclidean geometry principles.

Purpose: It helps students and geometry enthusiasts understand fundamental triangle properties and angle sum rules.

2. How Does the Calculator Work?

The calculator checks the triangle angle sum rule:

Where:

• All three angles must be positive numbers between 0° and 180°
• Their sum must exactly equal 180°
• Each angle must be less than 180°

Explanation: Three 90° angles sum to 270°, which violates the fundamental triangle angle sum theorem.

3. Importance of Triangle Angle Sum

Details: The 180° sum is a defining characteristic of Euclidean triangles. This rule is foundational for trigonometry and geometry.

4. Using the Calculator

Tips: Enter three angles (default 90° each) to see why three right angles can't form a triangle. Try other combinations to explore valid triangles.

5. Frequently Asked Questions (FAQ)

Q1: Why can't a triangle have three 90° angles?
A: Because 90° + 90° + 90° = 270° which exceeds the required 180° sum for all triangles.

Q2: Are there any geometries where this is possible?
A: Only in non-Euclidean geometries (spherical or hyperbolic), but not in standard plane geometry.

Q3: What's the maximum number of right angles in a triangle?
A: One. A triangle can have at most one 90° angle (right triangle).

Q4: What happens if the angles sum to less than 180°?
A: The "triangle" wouldn't close - it would be an open shape, not a valid triangle.

Q5: How does this relate to real-world applications?
A: Understanding these limitations is crucial in fields like architecture, engineering, and computer graphics.