CBSE Class 10 Math Question Paper 2018 Solution | Q25B

Question 25B: Prove that, in a right triangle, the square on the hypotenuse is equal to the sum of the square on the other two sides.

Video Explanation

Explanatory Answer | CBSE Class 10 Math 4 Mark Question 25B

Pythagoras theorem proof:
ABC is a right angled triangle right angled at B.
Draw BD perpendicular to AC.

By AA ΔABC is similar to ΔADB.
∴ \\frac{AB}{AD}) = \\frac{AC}{AB}) or AB² = AD × AC -----(1)
By AA ΔABC is similar to ΔBDC.
∴ \\frac{AC}{BC}) = \\frac{BC}{DC}) or BC² = AC × DC -----(2)

(1) + (2)
AB² + BC² = AD × AC + AC × DC
= AC (AD + DC)
The hypotenuse AC = (AD + DC)
So, AC (AD + DC) = AC × AC
Or AB² + BC² = AC²