CBSE 10th Math Sample Paper 2019 | Q25

This 2019 CBSE class 10 Maths 4 mark question is from Triangles. A standard NCERT text book question. Proving the Pythagoras Theorem.

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

Video Explanation

Explanatory Answer

Draw a right triangle ABC right angled at B.
We need to prove that AC² = AB² + BC²
Let us draw BD ⊥ AC
Theorem: If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.
ΔADB ~ ΔABC

So, \\frac{AD}{AB}) = \\frac{AB}{AC}) (Sides are proportional)
AD × AC = AB² ------ 1
Also ΔBDC ∼ ΔABC (Theorem)
So, \\frac{CD}{BC}) = \\frac{BC}{AC}) (Sides are proportional)
CD × AC = BC² ------ 2
Adding 1 and 2
AD × AC + CD × AC = AB² + BC²
AC(AD + CD) = AB² + BC²
AC × AC = AB² + BC²
AC² = AB² + BC²