# CBSE Class 10 Math Question Paper 2018 Solution | Q25B

###### CBSE Solved Question Paper 4 Mark | Pythagoras Theorem Proof

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.

## NCERT Solution to Class 10 Maths

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

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