Question

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.

Answer 1

Equation of Anjeli is true.

Step-by-step explanation:

Triangle ABC right angle at C such that

Considering AB = c as (Hypotenuse), AC = b as (Longer leg), BC = a as (Shorter leg)

Proof:

(a+b)² = c²+ 4(1/2) ab

In the Triangle ABC,  by Pythagoras theorem, Plugin the values we will get,

Hypotenuse² = longer leg² + shorter leg²

AB² = AC²+ BC²

c² = b²+ a² ------ q

(a+ b)² can be written using the identity as,

(a+ b)²= a² + 2ab + b² ----LHS

Plugin the above identity in the eq. q we will get,

c²+ 2ab = c² + (4/2) ab --- RHS

So LHS = RHS.

Hence proved.