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show that in a right angled triangles, the hypotenuse is the longest side.
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show that in a right angled triangles, the hypotenuse is the longest s...
In a triangle the sum of all angle is 180 .The side opposite to biggest angle is longest Hence if one angle is 90 the the sum of other two is 90 .hence other two angles are less than 90 . so longest side is opposite to 90 angle hence hypotenus is longest
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show that in a right angled triangles, the hypotenuse is the longest s...
Proof that the Hypotenuse is the Longest Side of a Right-Angled Triangle
A right-angled triangle is a triangle with one angle measuring 90 degrees. The longest side of a right-angled triangle is called the hypotenuse. To prove that the hypotenuse is the longest side, we need to use the Pythagorean Theorem.
Pythagorean Theorem
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's assume that a, b, and c are the lengths of the sides of a right-angled triangle, where c is the hypotenuse.
According to the Pythagorean Theorem,
c² = a² + b²
Proof
To prove that the hypotenuse is the longest side in a right-angled triangle, we need to show that c is greater than both a and b.
Let's assume that a is the longest side. In this case, we have:
a² = b² + c²
Now, we can rearrange the equation to get:
c² = a² - b²
Since a is the longest side, a > b. Therefore, a² > b².
Hence, we have:
c² = a² - b² > 0
This means that c is greater than 0. Therefore, c > 0.
So, we have shown that c is greater than both a and b, which means that the hypotenuse is the longest side in a right-angled triangle.
Conclusion
From the above proof, we can conclude that in a right-angled triangle, the hypotenuse is always the longest side. This is because the square of the hypotenuse is equal to the sum of the squares of the other two sides, and as a result, the hypotenuse will always be greater than both of the other two sides.
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show that in a right angled triangles, the hypotenuse is the longest side. for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about show that in a right angled triangles, the hypotenuse is the longest side. covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for show that in a right angled triangles, the hypotenuse is the longest side..
show that in a right angled triangles, the hypotenuse is the longest side. for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about show that in a right angled triangles, the hypotenuse is the longest side. covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for show that in a right angled triangles, the hypotenuse is the longest side..
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