Check if it’s a right triangle using the Pythagorean theorem: \( 7^2 + 24^2 = 25^2 \).
["Check if It’s a Right Triangle Using the Pythagorean Theorem: How to Verify with ( 7^2 + 24^2 = 25^2 )", "When working with right triangles, one of the most reliable methods to confirm it truly follows the geometric rules is by applying the Pythagorean Theorem. This powerful mathematical principle 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.", "A classic example to test this is the Pythagorean triple ( 7^2 + 24^2 = 25^2 ). Let’s break down how to verify this equation and determine whether the triangle is indeed right-angled.", "### What Is the Pythagorean Theorem?", "The Pythagorean Theorem defines the relationship:\n[ a^2 + b^2 = c^2 ]\nwhere:\n- ( a ) and ( b ) are the lengths of the two legs (the shorter sides),\n- ( c ) is the hypotenuse (the longest side, opposite the right angle).", "If the equation holds true, then the triangle must be right-angled.", "### Testing the Triangle with ( 7^2 + 24^2 = 25^2 )", "Let’s compute each side step by step:", "- ( 7^2 = 49 )\n- ( 24^2 = 576 )\n- ( 25^2 = 625 )", "Now add the squares of the two shorter sides:\n[ 49 + 576 = 625 ]", "Compare this sum to the square of the longest side:\n[ 625 = 625 ]", "Since both sides are equal, the Pythagorean Theorem is satisfied.", "### Conclusion: It’s a Right Triangle", "Because ( 7^2 + 24^2 = 25^2 ) holds true, the triangle formed by sides 7, 24, and 25 must be a right triangle, with 25 being the hypotenuse and the angle between 7 and 24 being the right angle.", "### Why Is This Important?", "Checking with the Pythagorean Theorem gives a quick and accurate way to verify right triangles without measuring all angles or sides manually. This method is widely used in geometry, construction, engineering, and physics, where accurate triangle properties are essential.", "So remember: if for a triangle with sides ( a ), ( b ), and ( c ), the equation ( a^2 + b^2 = c^2 ) holds true, you’ve confirmed it’s a right triangle — especially useful when you already know one side is the hypotenuse.", "---", "Key Takeaways:\n- Use ( a^2 + b^2 = c^2 ) to check for right triangles.\n- Verify carefully by squaring each side and confirming equality.\n- The equation ( 7^2 + 24^2 = 25^2 ) is a classic Pythagorean triple.\n- Confirming right angles helps in solving real-world geometry problems effectively.", "Catch those right angles fast — and always validate with the Pythagorean Theorem!"]
