in angle ABC if measurement of angle B is equal to 90 degree than a square + c square is equals to
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Pythagoras theorem states that in a right angled triangle, the square on the hypotenuse is equal to the sum of of the squares on the remaining two sides.
In triangle ABC, ∠B=90
o
and D is the mid-point of BC. JOin AD. Therefore, BD=DC
First, we consider the △ADB and applying
Pythagoras theorem we get,
AD
2
=AB
2
+BD
2
AB
2
=AD
2
−BD
2
...(i)
Similarly, we get from rt. angle triangles ABC we get,
AC
2
=AB
2
+BC
2
AB
2
=AC
2
−BC
2
...(ii)
Grom (i) and (ii),
AC
2
−BC
2
=AD
2
−BD
2
AC
2
=AD
2
−BD
2
+BC
2
AC
2
=AD
2
−BD
2
+BC
2
AC
2
=AD
2
−CD
2
+4CD
2
[BD=CD=
2
1
BC]
AC
2
=AD
2
+3CD
2
Hence Proved.
solution
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