Question

What are some key concepts of the pythagorean theorem:

a) The sum of the squares of the two shorter sides equals the square of the hypotenuse.
b) It applies only to right-angled triangles.
c) It can be used to find the distance between two points in a coordinate system.
d) All of the above.

Answer 1

The Pythagorean Theorem is a mathematical principle stating that in a right-angled triangle, the sum of the squares of the two shorter sides equals the square of the hypotenuse, and it can be used to calculate distances on a coordinate grid.

Step-by-step explanation:

The key concepts of the Pythagorean Theorem include: d) All of the above.

• The sum of the squares of the two shorter sides of a right triangle equals the square of the hypotenuse (a² + b² = c²).
• It applies exclusively to right-angled triangles.
• It can be leveraged to find the distance between two points on a coordinate system by forming a right triangle where the two points serve as corners of the triangle, and their distance as the hypotenuse.

Understanding and applying the Pythagorean theorem is a fundamental aspect of geometry and is useful in various practical and theoretical applications in mathematics and science.