Question

state and prove pyathagoras theorem

Answer 1

The Pythagorean Theorem states that, in a right triangle, the square of a (a2) plus the square of b (b2) is equal to the square of c (c2):a2 + b2 = c2
or Hypoteneous 2= perpendicular 2+ base 2
Note: 2 means square

Answer 2

THEOREM:  in a right angled triangle,the square of the hypotenuse is equalto the sum of the squares of the other two sides
GIVEN:in ΔABC,
           angleABC=90degree
TO PROVE: AC²=AB²+BC²
CONS:draw a perpendicular BD  from the vertex B,to the side AC. A-D-C.
PROOF:in right angled ΔABC,
            seg BD is perpendicular hyp AC
.:by similarity in right angled Δ,
ΔABC IS SIMILAR TO ΔADB IS SIMILAR TO ΔBDC
NOW, ΔABC SIMILAR ΔADB
.:AB/AD=AC/AB              (csct)
.:AB²=AC *AD                           (1)
ALSO,ΔABC SIMILAR ΔBDC
.:BC/DC=AC/BC             (csct)
.:BC²=DC*AC                             (2)
from 1 and 2,
AB²+BC²=AC*AD+AC*DC
             =AC*(AD+DC)
             =AC*AC                         (A-D-C)
.:AB²+BC²=AC² i.e AC²=AB²+BC²