No, the Pythagorean Theorem only applies to right triangles.
Understanding the Pythagorean Theorem
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (legs).
- Formula: a² + b² = c²
- Where 'a' and 'b' are the lengths of the legs, and 'c' is the length of the hypotenuse.
Why It Only Applies to Right Triangles
The Pythagorean Theorem is based on the geometric relationship between the sides of a right triangle. This relationship doesn't hold true for other types of triangles, such as acute or obtuse triangles.
- Acute Triangles: Have all angles less than 90 degrees.
- Obtuse Triangles: Have one angle greater than 90 degrees.
In these triangles, the relationship between the sides is different, and the Pythagorean Theorem does not apply.
Examples:
- Right Triangle: If a right triangle has legs of length 3 and 4, the hypotenuse will have a length of 5 (3² + 4² = 5²).
- Acute Triangle: If an acute triangle has sides of length 3, 4, and 5, the Pythagorean Theorem does not hold true (3² + 4² ≠ 5²).
