Expalin and Prove The Pythagoras Theorem
Answers
Answer:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
^ -- symbolize Square
Pythagoras Theorem Formula-
Consider the triangle given above:
Where “a” is the perpendicular side,
“b” is the base,
“c” is the hypotenuse side.
Hypotenuse^2 = Perpendicular^2 + Base^2
c^2 = a^2 + b^2
Step-by-step explanation:
^ -- symbolize Square
Proof:
Pythagoras Theorem Proof
Given: A right-angled triangle ABC.
To Prove- AC^2 = AB^2 + BC^2
Proof:
First, we have to drop a perpendicular BD onto the side AC
We know, △ADB ~ △ABC
Therefore, ADAB=ABAC (Condition for similarity)
Or, AB^2 = AD × AC ……………………………..……..(1)
Also, △BDC ~△ABC
Therefore, CDBC=BCAC (Condition for similarity)
Or, BC^2= CD × AC ……………………………………..(2)
Adding the equations (1) and (2) we get,
AB^2 + BC^2 = AD × AC + CD × AC
AB^2 + BC^2 = AC (AD + CD)
Since, AD + CD = AC
Therefore, AC^2 = AB^2 + BC^2
Hence, the Pythagorean thoerem is proved.
hi mate,
Pythagoras Theorem Proof
Given: A right-angled triangle ABC.
To Prove- AC² = AB² + BC²
Proof: First, we have to drop a perpendicular BD onto the side AC
We know, △ADB ~ △ABC
Therefore,
AD AB
----- = -----
AB AC
(Condition for similarity)
Or, AB² = AD × AC …………………..……..(1)
Also, △BDC ~△ABC
Therefore,
CD BC
----- = -----
BC AC
(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.
i hope it helps you.
