Question

Please Help It Is Past Due!

Answer 1

Explanation:

First we consider ΔABC and ΔBCD,

∠C=∠C  (common)

∠B=∠D=$90\textdegree$

So, ΔABC ≈ ΔBCD (By AA similarity rule )

So by taking corresponding sides in ratios we get

$\frac{AB}{BD}=\frac{AC}{BC}=\frac{BC}{CD}$      

Now

$AC.CD=BC.BC\\BC^{2} =AC.CD$              -------- Eqn (1)

Similarly,

We consider ΔABD and ΔABC

∠A=∠A (Commom)

∠B=∠D=$90\textdegree$

So,

ΔABD ≈ ΔABC (By AA similarity rule )

So by taking corresponding sides in ratios we get

$\frac{BC}{BD}=\frac{AC}{AB}=\frac{AB}{AD}$  

Now,

$AB.AB=AC.AD\\AB^{2} =AC.AD$              --------Eqn (2)

By Adding both the equation we get

$AB^2+BC^2=AC.CD+AC.AD\\AB^2+BC^2=AC(CD+AD)\\AB^2+BC^2=AC.AC\\AB^2+BC^2=AC^2$

Hence, we proved the pythagorean theorem by using similarity of triangle.