Chapter 6 · Question 6

State Pythagoras theorem and its converse.

Answer

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides:

c^2=a^2+b^2

. Conversely, if one side square equals the sum of squares of the other two sides, the triangle is right-angled.

Right triangle formula: hypotenuse squared equals sum of other two squares.

If

\triangle ABC

is right-angled at

B

, then

AC^2=AB^2+BC^2

. Conversely, if in a triangle

AC^2=AB^2+BC^2

, then the angle opposite

AC

is a right angle. NCERT uses similarity of triangles to prove this result.

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: $c^2=a^2+b^2$ .