explain pythagorus theorem in geometry class 9
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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 (legs). Here, 'a' and 'b' represent the lengths of the two legs, and 'c' represents the length of the hypotenuse.
Step 2: Identify Sides of a Right-Angled Triangle
In a right-angled triangle, the hypotenuse (c) is always the longest side and is opposite the 90∘ angle. The other two sides, a and b, are called the legs or cathetus, and they form the right angle.
Step 3: Illustrate with an Example
Let's consider a right-angled triangle where the lengths of the two legs are 3 units and 4 units. We want to find the length of the hypotenuse using the Pythagorean Theorem.
Step 4: Apply the Formula
Substitute the given values of a and b into the Pythagorean theorem equation. This will allow us to calculate the square of the hypotenuse.
Step 5: Substitute Values and Calculate
We substitute a=3 and b=4 into the formula. First, we square both values: 32=9 and 42=16. Then, we add these squared values: 9+16=25.
Step 6: Find the Hypotenuse Length
To find the length of the hypotenuse c, we take the square root of 25. The result is 5. Therefore, the hypotenuse of this right-angled triangle is 5 units long.