Question

ABCD is an isosceles triangle right angled at C , prove that AB^2 = 2AC^2

Answer 1

Step-by-step explanation:

If its an Isosceles triangle then

AC = BC ..........(I)

and you told that it is right angled at C

So, from Pythagoras Theorem

h^2 = p^2 + b^2

(AB)^2 = (BC)^2 + (AC)^2 from (I)

(AB)^2 = 2(AC)^2

PROVED!!

Thank u!

Answer 2

QUESTION:

ABC is an isosceles triangle right angled at C , prove that AB^2 = 2AC^2 :

ANSWER:

TO PROVE:

${ab}^{2} = {ac}^{2} .....(eq.1)$

PROOF:

AC= BC (AS IT'S A ISCOSCLES TRIANGLE)

IN TRIANGLE ABC:

${ac}^{2} + {bc}^{2} = {ab}^{2} \\ (by \: pythagores \: therom)$

NOW;

${ac}^{2} + {ac}^{2} = {ab}^{2} \\ (from \: eq.1){as \: ac = bc}$

$2 {ac}^{2} = {ab}^{2}$

HENCE PROVED

AB^2 = 2AC^2 .

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