explain pythagorus theorem in geometry standard 9 run dynamic unique A
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Step-by-Step Solution
Step 1: State the Pythagorean Theorem
The Pythagorean theorem states that in a right-angled 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. These two sides are often called legs. This fundamental relationship holds true for all right-angled triangles.
Step 2: Identify Sides of a Right Triangle
In a right triangle, we label the two shorter sides as 'a' and 'b'. These sides form the right angle. The longest side, which is always opposite the right angle, is labeled 'c' and is known as the hypotenuse. It's crucial to correctly identify these sides before applying the theorem.
Step 3: Illustrate with an Example
Let's consider a right-angled triangle with legs of length 3 units and 4 units. According to the theorem, the square of the hypotenuse must be equal to the sum of the squares of these two legs. We substitute the values of 'a' and 'b' into the formula to find 'c'.
Step 4: Calculate the Hypotenuse
We calculate the squares of the leg lengths: 32=9 and 42=16. Adding these values, we get 9+16=25. To find the length of the hypotenuse 'c', we take the square root of 25, which gives us 5. Therefore, the hypotenuse of this triangle is 5 units long.