Anjeli writes the equation (a+b)2=c2+4(12ab) to begin a proof of the Pythagorean theorem.

Use the drop-down menus to explain why this is a true equation.

Therefore Anjeli is correct and

 is TRUE.

Step-by-step explanation:

Given:

Label on triangle as ΔABC right angle at C such that

AB = c  .....(Hypotenuse)

AC = b  ....(Longer leg)

BC = a  ....(Shorter leg)

To Prove:

Proof:

We know, in Right angle triangle ABC by Pythagoras theorem we get,

Substituting the values we get

   ...............( 1 )

Now the Left hand side of what Anjeli wrote is

Left hand side = (a+b)²

 Using identity (A+B)² = A²+ B² + 2AB we get

Left hand side = a²+ b² + 2ab

From ( 1 ) we have

Substituting we get

Left hand side = c² + 2ab        ...........................( 2 )

Now,

Right hand side =

Dividing 4 by 2 we get  2, hence

Right hand side =  .........................( 3 )

Therefore,

Left hand side = Right hand side          From  ( 2 ) and ( 3 )

     ..True

Therefore Anjeli is correct and

 is TRUE.

image for option 4

step-by-step explanation:

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yes they are the same