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Results Deduced From Pythagoras Theorem

Triangles II - Concepts

Calculating Perimeter of Triangle

Area of Similar Triangles

Similarity Related To Right Triangle

Pythagoras Theorem

Results Deduced From Pythagoras Theorem

Class - RRB Technician Grade I Signal Subjects

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 $large AC^2= AB^2 +BC^2+2BC. BD$

Given: $large Delta$ 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 is such that $angle B=150^{0}$ and $ADperp CB$ and AB = 4 cm, BC = 3 cm, BD = 2 cm. Then Find AC.
A. $sqrt{37}$		B. $sqrt{33}$
C. $sqrt{47}$		D. $sqrt{43}$
Right Option : A
View Explanation

Question : 2

If is such that $angle B=120^{0}$ and and AC= 12 cm, AB = 4 cm, BD = 2 cm. Then Find BC.
A. $-2+2sqrt {33}$	B. $-2- 2sqrt{33}$	C. $-2pm 2 sqrt{33}$	D. none of these
Right Option : A
View 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.
A. $sqrt{306}$	B. $sqrt{294}$	C. $sqrt{304}$	D. $sqrt{294}$
Right Option : C
View Explanation

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Attention !!!!!

Results Deduced From Pythagoras Theorem

Results Deduced From Pythagoras Theorem

Students / Parents Reviews [10]

Archit Segal

Aman Kumar Shrivastava

Barkha Arora

Manish Kumar

Cheshta

Eshan Arora

Ayan Ghosh

Shreya Shrivastava

Om Umang

Prisha Gupta