Math, asked by nyeleti, 11 months ago

how to prove the pythagoras theorem

Answers

Answered by loveguru38
2

Answer:

Here your answer.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2

Step-by-step explanation:

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Answered by Suriddhim
1

Pythagoras Theorem ProofGiven: A right-angled triangle ABC.To Prove- AC2 = AB2 + BC2Proof: First, we have to drop a perpendicular BD onto the side AC

Proof: First, we have to drop a perpendicular BD onto the side AC

Proof: First, we have to drop a perpendicular BD onto the side ACWe know, △ADB ~ △ABC

Proof: First, we have to drop a perpendicular BD onto the side ACWe know, △ADB ~ △ABCTherefore, ADAB=ABAC (Condition for similarity)

Proof: First, we have to drop a perpendicular BD onto the side ACWe know, △ADB ~ △ABCTherefore, ADAB=ABAC (Condition for similarity)Or, AB2 = AD × AC ……………………………..……..(1)

Proof: First, we have to drop a perpendicular BD onto the side ACWe know, △ADB ~ △ABCTherefore, ADAB=ABAC (Condition for similarity)Or, AB2 = AD × AC ……………………………..……..(1)Also, △BDC ~△ABC

Proof: First, we have to drop a perpendicular BD onto the side ACWe know, △ADB ~ △ABCTherefore, ADAB=ABAC (Condition for similarity)Or, AB2 = AD × AC ……………………………..……..(1)Also, △BDC ~△ABCTherefore, CDBC=BCAC (Condition for similarity)

Proof: First, we have to drop a perpendicular BD onto the side ACWe know, △ADB ~ △ABCTherefore, ADAB=ABAC (Condition for similarity)Or, AB2 = AD × AC ……………………………..……..(1)Also, △BDC ~△ABCTherefore, CDBC=BCAC (Condition for similarity)Or, BC2= CD × AC ……………………………………..(2)

Proof: First, we have to drop a perpendicular BD onto the side ACWe know, △ADB ~ △ABCTherefore, ADAB=ABAC (Condition for similarity)Or, AB2 = AD × AC ……………………………..……..(1)Also, △BDC ~△ABCTherefore, CDBC=BCAC (Condition for similarity)Or, BC2= CD × AC ……………………………………..(2)Adding the equations (1) and (2) we get,

Proof: First, we have to drop a perpendicular BD onto the side ACWe know, △ADB ~ △ABCTherefore, ADAB=ABAC (Condition for similarity)Or, AB2 = AD × AC ……………………………..……..(1)Also, △BDC ~△ABCTherefore, CDBC=BCAC (Condition for similarity)Or, BC2= CD × AC ……………………………………..(2)Adding the equations (1) and (2) we get,AB2 + BC2 = AD × AC + CD × AC

Proof: First, we have to drop a perpendicular BD onto the side ACWe know, △ADB ~ △ABCTherefore, ADAB=ABAC (Condition for similarity)Or, AB2 = AD × AC ……………………………..……..(1)Also, △BDC ~△ABCTherefore, CDBC=BCAC (Condition for similarity)Or, BC2= CD × AC ……………………………………..(2)Adding the equations (1) and (2) we get,AB2 + BC2 = AD × AC + CD × ACAB2 + BC2 = AC (AD + CD)

Proof: First, we have to drop a perpendicular BD onto the side ACWe know, △ADB ~ △ABCTherefore, ADAB=ABAC (Condition for similarity)Or, AB2 = AD × AC ……………………………..……..(1)Also, △BDC ~△ABCTherefore, CDBC=BCAC (Condition for similarity)Or, BC2= CD × AC ……………………………………..(2)Adding the equations (1) and (2) we get,AB2 + BC2 = AD × AC + CD × ACAB2 + BC2 = AC (AD + CD)Since, AD + CD = AC

Proof: First, we have to drop a perpendicular BD onto the side ACWe know, △ADB ~ △ABCTherefore, ADAB=ABAC (Condition for similarity)Or, AB2 = AD × AC ……………………………..……..(1)Also, △BDC ~△ABCTherefore, CDBC=BCAC (Condition for similarity)Or, BC2= CD × AC ……………………………………..(2)Adding the equations (1) and (2) we get,AB2 + BC2 = AD × AC + CD × ACAB2 + BC2 = AC (AD + CD)Since, AD + CD = ACTherefore, AC2 = AB2 + BC2

Hence, the Pythagorean thoerem is proved.

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