Question

What is inverse of Pythagoras theorem???

Answer 1

Thanks for asking the question!

ANSWER::

INVERSE PYTHAGORAS THEOREM

To prove - If in a triangle the square on one of the sides equals the sum of the squares on the remaining two sides of the triangle, then the angle contained by the remaining two sides of the triangle is right.

Proof - Let there be a triangle ABC

BC² = BA² + AC²

After this , draw AD at right angles to AC

Make DA =AB

Join DC

Now , DA = AB

So , DA² = AB²

And , DA² + AC² = AB² + AC²

DC² = DA² + AC²

BC² = BA² + AC²

DC² = BC²

So, DC = BC

And , Triangles ABC and ADC are congruent

AB=AD

BC=DC

AC=AC (common)

∠CAD =∠CAB = 90°

Hop it helps!

Answer 2

.INVERSE PYTHAGORAS THEOREM___

TO PROVE-If in a triangle the square on of the side equal the sum of the square on the remaining two side of the triangle, then the angle contain by the remaining two sides of the triangle is right.

Proof let there be a triangle ABC

${bc}^{2} \: = {ba }^{2} + {ac}^{2}$
After this, draw AD at right angles to AC, MAKE DA=AB
JOIN DC
now, DA=AB
SO, DA SQ = AB SQ

AND,
${da}^{2} + {ac}^{2} = {ab }^{2} + {ac}^{2}$
Bc sq = ba sq + ac sq
So, DC=BC

AND TRIANGLE ABC AND TRIANGLE ADC ARE CONGRUENT

AB=AD
BC=DC
angle CAD= angle CAB= 9
AC=AC (COMMON)