Question

Congruency of triangles and phytagoras theorem

Answer 1

Pythagoras theorem is that theorem in which the base square and perpendicular square = hypteneous

Answer 2

Answer:

Pythagoras stated relationship among 3 sides in a right triangle,& also in an obtuse triangle & an acute triangle too… But Pythagoras Theorem is the relationship in a right triangle… & the other two are extensions of Pythagoras theoram…. as these 2 are proved by the right triangle theorem.

The theorem is stated as follows:

(1) In any right triangle the square of the hypotenuse is equal to the sum of the squares of the other 2 sides.

ie, if we construct a square on the hypotenuse another squares on the other two sides of the triangle.

Then area( square on the hypotenuse) = area( square on the base) + area( square on the perpendicular)

Like in right triangle ABC right angled at ‘B'

AC²= AB² + BC²……………(1)

(2) Now the extension of Pythagoras theorem in an obtuse triangle ABC , obtuse angled at B is→

AC²= AB²+ BC² + 2BC.BX ( where BX is the projection of AB on BC

(3) Now the extension of Pythagoras theorem in an acute triangle ABC, considering AC side opposite to acute angle B is→

AC²= AB² + BC² - 2BC.BX ( where BX is the projection of AB on BC.