what is the Pythagoras theorem
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Pythagoras theorem states that in a right angle triangle the square of the side opposite to the right angle which is called hypotenuse is equal to the sum of the squares of other two sides which are base and height.
hope this helps :-)
hope this helps :-)
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Theorem - In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given: In a right angled 3ABC, +A = 90c.
To prove: BC 2 = AB 2 + AC 2
Construction: Draw AD⊥ BC
Proof: In triangles ABC and DBA, B is the common angle.
Also, we have 0
ΔABC ~ ΔDBA (AA similarity criterion)
Thus, their corresponding sides are proportional.
Hence, AD/DB = BC/BA
AB 2 = DB * BC (1)
Similarly, we have ΔABC ~ ΔDAC.
Thus, BC/AC =AC/DC
AC 2 = BC*DC (2)
Adding (1) and (2) we get,
AB 2 + AC 2 = DB * BC + BC*DC
= BC (DB + DC)
= BC * BC = BC 2
Thus BC 2 = AB 2 + AC 2
Given: In a right angled 3ABC, +A = 90c.
To prove: BC 2 = AB 2 + AC 2
Construction: Draw AD⊥ BC
Proof: In triangles ABC and DBA, B is the common angle.
Also, we have 0
ΔABC ~ ΔDBA (AA similarity criterion)
Thus, their corresponding sides are proportional.
Hence, AD/DB = BC/BA
AB 2 = DB * BC (1)
Similarly, we have ΔABC ~ ΔDAC.
Thus, BC/AC =AC/DC
AC 2 = BC*DC (2)
Adding (1) and (2) we get,
AB 2 + AC 2 = DB * BC + BC*DC
= BC (DB + DC)
= BC * BC = BC 2
Thus BC 2 = AB 2 + AC 2
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