Results Deduced From Pythagoras Theorem


 
 
Concept Explanation
 

Results Deduced From Pythagoras Theorem

Result 1 : In the given large Delta ABC, obtuse angled at B if AD large perp CB produced, then large AC^2= AB^2 +BC^2+2BC. BD

Givenlarge Delta ABC obtuse angled at B if AD large perp CB produced,

To Prove: large AC^2= AB^2 +BC^2+2BC. BD

Proof:

  In large Delta ADB right angled at D

large AB^2= AD^2+BD^2       [ By Pythagoras Theorem ]            .........(1)

In large Delta ADC right angled at D

large AC^2= AD^2+CD^2       [ By Pythagoras Theorem ]

large AC^2= AD^2+(BD + BC) ^2

large AC^2= AD^2+BD^2 + BC^2+ 2 BD.BC

large AC^2= (AD^2+BD^2 )+ BC^2+ 2 BD.BC

large AC^2= AB^2 + BC^2+ 2 BD.BC         [From Equation 1]

 

Result 2 : In the given large Delta ABC, if angle B is an acute angle and  AD large perp BC, then large large AC^2= AB^2 +BC^2-2BC. BD

Given: In large Delta ABC  angle B is an acute angle and  AD large perp BC,

To Prove: large AC^2= AB^2 +BC^2-2BC. BD

Proof:   In large Delta ADB right angled at D

large AB^2= AD^2+BD^2       [ By Pythagoras Theorem ]            .........(1)

In large Delta ADC right angled at D

large AC^2= AD^2+CD^2       [ By Pythagoras Theorem ]

large AC^2= AD^2+(BC -BD) ^2

large AC^2= AD^2+BD^2 + BC^2 - 2 BD.BC

large AC^2= (AD^2+BD^2 )+ BC^2 - 2 BD.BC

large AC^2= AB^2 + BC^2 - 2 BD.BC  From Equation (1)

Sample Questions
(More Questions for each concept available in Login)
Question : 1

If bigtriangleup ABC is such that angle B=150^{0} and ADperp CB and AB = 4 cm, BC = 3 cm, BD = 2 cm. Then Find AC.

Right Option : A
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Explanation
Question : 2

If bigtriangleup ABC is such that angle B=120^{0}and ADperp CB and AC= 12 cm, AB = 4 cm, BD = 2 cm. Then Find BC.

Right Option : A
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Explanation
Question : 3

If bigtriangleup ABC  is such that angle B=45^{0} and ADperp CB and AB = 17 cm, BC = 15 cm, BD = 7 cm. Then Find AC.

Right Option : C
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Explanation
 
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