Which theorem is always applicable to right triangles?

Which theorem is always applicable to right triangles?

• A. Pythagorean theorem
• B. Euclidean theorem
• C. Congruence theorem
• D. Trigonometric theorem

Answer: (A)

The Pythagorean theorem is always applicable to right triangles because it specifically relates to their geometric properties. This theorem states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This relationship is foundational in understanding the properties of right triangles and is used extensively in various applications, including finding distances and solving problems involving right-angled triangles. The theorem forms the basis for many aspects of geometry and is a critical tool in various mathematical fields beyond basic geometry, such as trigonometry and algebra. Its universal applicability to all right triangles regardless of their dimensions is what makes it a fundamental theorem in mathematics.

The Pythagorean theorem is always applicable to right triangles because it specifically relates to their geometric properties. This theorem states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This relationship is foundational in understanding the properties of right triangles and is used extensively in various applications, including finding distances and solving problems involving right-angled triangles.

The theorem forms the basis for many aspects of geometry and is a critical tool in various mathematical fields beyond basic geometry, such as trigonometry and algebra. Its universal applicability to all right triangles regardless of their dimensions is what makes it a fundamental theorem in mathematics.