First, check if it is a right triangle using the Pythagorean theorem: \( 7^2 + 24^2 = 49 + 576 = 625 \) and \( 25^2 = 625 \).
["How to Determine If a Triangle Is a Right Triangle Using the Pythagorean Theorem", "Identifying whether a triangle is a right triangle is a fundamental skill in geometry. One of the most reliable methods is the Pythagorean theorem, which provides a simple way to verify if a triangle has a right angle. In this article, we’ll walk through the process step-by-step using a classic example: confirming whether a triangle with sides 7, 24, and 25 is a right triangle.", "---", "### What Is the Pythagorean Theorem?", "The Pythagorean 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 other two sides. Symbolically, it is written as:", "[\na^2 + b^2 = c^2\n]", "where ( c ) is the hypotenuse, and ( a ) and ( b ) are the other two sides.", "If the equation holds true for the given side lengths, the triangle is a right triangle. If not, it is not a right triangle.", "---", "### Step-by-Step Check Using the Example: 7, 24, and 25", "#### Step 1: Identify the longest side\nSince the hypotenuse is always the longest side in a right triangle, we first determine which side is the largest:", "- Side 1: ( 7 )\n- Side 2: ( 24 )\n- Side 3 (hypotenuse candidate): ( 25 )", "Clearly, ( 25 ) is the largest — this confirms it could be the hypotenuse.", "#### Step 2: Square each side\nNext, we compute the squares of all three sides:", "[\n7^2 = 49\n]\n[\n24^2 = 576\n]\n[\n25^2 = 625\n]", "#### Step 3: Apply the Pythagorean equation\nNow we check whether the sum of the squares of the two shorter sides equals the square of the hypotenuse:", "[\n7^2 + 24^2 = 49 + 576 = 625\n]\n[\n25^2 = 625\n]", "Since both sides equal ( 625 ), the equation holds true:", "[\n49 + 576 = 625\n]", "---", "### Conclusion: It Is a Right Triangle!", "Because ( 7^2 + 24^2 = 25^2 ), the triangle with sides measuring 7, 24, and 25 is indeed a right triangle. This means it has one 90-degree angle, and the side of length 25 is the hypotenuse.", "---", "### Why This Matters", "Recognizing right triangles is essential for geometry, trigonometry, architecture, and many practical applications. Using the Pythagorean theorem gives a quick, accurate test — even for complex problems — ensuring shape validity before further calculations.", "If you’re ever unsure whether a triangle is right-angled, remember:\n✅ Square all three side lengths\n✅ Test the sum of the smaller squares against the largest\n✅ If equal, it’s a right triangle!", "---", "Keywords for SEO: right triangle test, Pythagorean theorem examples, how to check right triangle, check triangle type, math geometry problem, verify right angle, apply Pythagorean theorem, 7-24-25 triangle right angle, triangle angle identification."]
