Check if it's a right triangle: \( 7^2 + 24^2 = 49 + 576 = 625 = 25^2 \).
["# How to Check if It’s a Right Triangle: Proven with ( 7^2 + 24^2 = 25^2 )", "Understanding right triangles is fundamental in geometry, and one of the fastest ways to verify if a triangle is right-angled is using the Pythagorean Theorem. This simple yet powerful principle states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides.", "The Pythagorean Theorem Formula:", "[\na^2 + b^2 = c^2\n]", "Where:\n- ( a ) and ( b ) are the lengths of the legs of the triangle,\n- ( c ) is the length of the hypotenuse (the longest side).", "## A Classic Example: ( 7^2 + 24^2 = 25^2 )", "Let’s apply this concept step-by-step using the numbers 7², 24², and 25².", "1. Calculate the squares of the two smaller sides:\n ( 7^2 = 49 )\n ( 24^2 = 576 )", "2. Add these values:\n ( 49 + 576 = 625 )", "3. Take the square of the side opposite the right angle:\n ( 25^2 = 625 )", "Now, observe:\n[\n7^2 + 24^2 = 625 = 25^2\n]", "Since the sum of the squares of the two legs equals the square of the third side, this confirms that the triangle with side lengths 7, 24, and 25 is indeed a right triangle, with 25 as the hypotenuse.", "## Why This Method Works", "This approach avoids complex angle measurements or trigonometric calculations, making it quick and accessible for students and anyone studying geometry. As long as the equation matches exactly, the triangle must be right-angled.", "## Visual Tip: Drawing It Out", "Imagine or sketch a right triangle with legs 7 and 24 units. The hypotenuse would naturally span 25 units, visually confirming the equality. This mental model strengthens conceptual understanding.", "## Conclusion", "To check if a triangle is right-angled, directly apply the Pythagorean Theorem. The case of ( 7^2 + 24^2 = 25^2 ) is a perfect example—simple, verifiable, and foundational in geometry. Use this method confidently to identify right triangles every time!", "---", "Keywords: right triangle, Pythagorean theorem, verify triangles, geometry tutorial, (7^2 + 24^2 = 25^2), teach geometry, right triangle example, check triangle type, 90-degree triangle proof", "Meta Description: Learn how to check if a triangle is a right triangle using the Pythagorean Theorem with the example (7^2 + 24^2 = 25^2). Step-by-step guide to apply (a^2 + b^2 = c^2) effectively."]
