   Question Answers

# $ABC$ is an isosceles triangle with $AC = BC$. If $A{B^2} = 2A{C^2}$, prove that $ABC$ is a right angled triangle.  Hint – Use Pythagoras theorem and make a diagram . Given, $\Delta ABC$ is an isosceles triangle .
Also given $AC = BC....(1)$
Also, given that
${(AB)^2} = 2{(AC)^2}$
Using Pythagora's theorem, where square of hypotenuse is equal to sum of the square of other two sides of the right angled triangle.
$\therefore \;{(AB)^2} = {(AC)^2} + {(AC)^2}.....(2)$
Therefore,
From (1) and (2),
${(AB)^2} = {(AC)^2} + {(BC)^2}$
Hence , By converse of Pythagoras theorem triangle $ABC$ is an isosceles right angled triangle.

Note - In these types of questions of isosceles triangles are those whose two sides are equal .Right angled triangle can also be isosceles . Here we have proved the questions by converse of Pythagoras theorem.
Isosceles Triangle Formula  CBSE Class 10 Maths Chapter 6 - Triangles Formula  Types of AC Motors  The Difference Between an Animal that is A Regulator and One that is A Conformer  Phasor Representation Ac  CBSE Class 7 Maths Chapter 6 - Triangle and Its Properties Formulas  AC Voltage Applied to Series LCR Circuit  Right Angled Triangle Constructions  CBSE Class 10 Maths Chapter 10 - Circles Formula  CBSE Class 10 Maths Chapter 2 - Polynomials Formula  Important Questions for CBSE Class 7 English An Alien Hand Chapter 10 - An Alien Hand  Important Questions for CBSE Class 10 Maths & Science with Answers  Important Questions for CBSE Class 10 Maths Chapter 6 - Triangles  Important Questions for CBSE Class 10 Maths, Chapter wise Questions with Answers  Important Questions for CBSE Class 7 English An Alien Hand  Important Questions for CBSE Class 10 Maths Chapter 10 - Circles  Important Questions for CBSE Class 10 Science, Chapter wise Questions with Answers  Important Questions for CBSE Class 6 English A Pact with The Sun Chapter 10 - A Strange Wrestling Match  Important Questions for CBSE Class 10 Maths Chapter 2 - Polynomials  Important Questions for CBSE Class 10 Maths Chapter 11 - Constructions  CBSE Previous Year Question Papers Class 10 Maths with Solutions  CBSE Class 10 Maths Question Paper 2019 with Solutions - Free PDF  CBSE Class 10 Hindi A Question Paper with Solutions  CBSE Class 10 English Communicative Question Paper with Solutions  CBSE Class 10 Hindi B Question Paper with Solutions  CBSE Class 10 Maths Question Paper 2017  CBSE Class 10 Maths Question Paper 2020  CBSE Class 10 Science Board Question Paper 2019 with Solutions  Maths Question Paper for CBSE Class 10 - 2011  Maths Question Paper for CBSE Class 10 - 2008  NCERT Solutions for Class 10 Maths Chapter 6 Triangles  RS Aggarwal Class 10 Solutions - Triangles  RD Sharma Solutions for Class 9 Maths Chapter 10 - Congruent Triangles  RD Sharma Solutions for Class 10 Maths Chapter 4 - Triangles  RS Aggarwal Class 9 Solutions Chapter-9 Congruence of Triangles and Inequalities in a Triangle  NCERT Solutions for Class 7 English An Alien Hand Chapter-10  NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and Its Properties  NCERT Solutions for Class 6 English A pact with the Sun Chapter-10  RD Sharma Solutions for Class 9 Maths Chapter 9 - Triangle and its Angles  NCERT Exemplar for Class 10 Maths Chapter 6 - Triangles (Book Solutions)  