First, verify if the triangle is a right triangle. Check if \( 7^2 + 24^2 = 25^2 \):

["# How to Verify If a Triangle Is a Right Triangle: Using the Pythagorean Theorem", "Determining whether a triangle is a right triangle is a fundamental skill in geometry. Whether you're solving math problems, teaching students, or exploring geometric principles, applying the Pythagorean Theorem provides a clear and reliable method. This article shows you how to verify if a triangle is right-angled by checking the relationship among its side lengths: ( a^2 + b^2 = c^2 ), where ( c ) is the longest side.", "---", "## Step 1: Identify the Longest Side", "To begin, label all three sides of the triangle. In any triangle, the side with the greatest length is called the hypotenuse if the triangle is right-angled. If you don’t know which side is the longest, compare the squared lengths:", "- Calculate ( 7^2 = 49 )\n- ( 24^2 = 576 )\n- ( 25^2 = 625 )", "Clearly, ( 25^2 > 24^2 + 7^2 ), so 25 is the longest side if this triangle is a right triangle.", "---", "## Step 2: Apply the Pythagorean Theorem", "The Pythagorean Theorem states that in a right triangle:", "[\na^2 + b^2 = c^2\n]", "Where ( c ) is the hypotenuse (the longest side), and ( a ) and ( b ) are the other two sides.", "Plug in your values:", "[\n7^2 + 24^2 = 49 + 576 = 625\n]", "Then compute:", "[\n25^2 = 625\n]", "---", "## Step 3: Confirm the Equality", "Since\n[\n7^2 + 24^2 = 625 = 25^2\n]", "the equation holds true. This confirms that the triangle with side lengths 7, 24, and 25 satisfies the Pythagorean condition.", "---", "## Conclusion: It’s a Right Triangle", "You’ve now verified the triangle is right-angled because the squares of the two shorter sides add up exactly to the square of the longest side. This method is straightforward and works for any triangle where you know all three side lengths.", "Recap:\n- Identify the longest side\n- Compute squares of all three sides\n- Check if ( a^2 + b^2 = c^2 ) \nOnce verified, you confirm a right triangle — a key milestone in geometry!", "---", "### Why This Matters", "Understanding how to identify right triangles helps solve real-world problems—from calculating diagonal distances in maps and architecture to physics and engineering applications. Plus, mastering the Pythagorean Theorem builds a foundation for advanced math topics like trigonometry and coordinate geometry.", "Start practicing with different side combinations to become confident in recognizing right triangles every time.", "---", "Keywords: right triangle, Pythagorean theorem, verify right triangle, 7^2 + 24^2 = 25^2, geometry, triangle properties, math tutorial, diagonal calculation, geometry basics."]