pythagoras theorem assignment for 10th
Answers
Answer:
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangles have been named as Perpendicular, Base and Hypotenuse.
Step-by-step explanation:
” is the perpendicular side,
“b” is the base,
“c” is the hypotenuse side.
According to the definition, the Pythagoras Theorem formula is given as:
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
Given: A right-angled triangle ABC.
To Prove- AC2 = AB2 + BC2
Pythagoras Theorem Proof
Proof: First, we have to drop a perpendicular BD onto the side AC
We know, △ADB ~ △ABC
Therefore, ADAB=ABAC (Condition for similarity)
Or, AB2 = AD × AC ……………………………..……..(1)
Also, △BDC ~△ABC
Therefore, CDBC=BCAC (Condition for similarity)
Or, BC2= CD × AC ……………………………………..(2)
Adding the equations (1) and (2) we get,
AB2 + BC2 = AD × AC + CD × AC
AB2 + BC2 = AC (AD + CD)
Since, AD + CD = AC
Therefore, AC2 = AB2 + BC2
Hence, the Pythagorean thoerem is proved
Step-by-step explanation:
Ac2 =Ab2+Ac2. in right ABC ac is hypoentuse