Question

Which is the last sentence of the proof?

Answer 1

Letra c, pois A2+B2=C2 e para completar a multiplicação de c x ... é c então c=f+e

Answer 2

Answer:

Because f+e=c, $a^2+b^2=c^2$.

Step-by-step explanation:

Given $\triangle ABC$ and $\triangle CBD$ are right triangles.

To prove that $a^2+b^2=c^2$

Because $\triangle ABC\; and \;\triangle CBD$   both have a right angle. It means  one angle of both triangle is of$90^{\circ}$.

And tha angle B is same in both triangles .Therefore, triangles must be similar by AA similarity.

Similarly ,  $\triangle ABC$ and $\triangle CBD$  are both right triangles and angle A is common in both triangles . So , they are similar by AA similarity .

Similarity: When two triangles are simialr then their corresponding angles are equal and their corresponding sides are in equal proportion.

Therefore , the two proportions can be rewritten as

$a^2=cf$  ( I equation )

$b^2=ce$ ( II equation )

Adding $b^2$ on both side of I equation  then we  can write equation I as

$a^2+b^2=b^2+cf$

$a^2+b^2= ce+cf$

Because $b^2$ and ce are equal and substitute on the right side of equation I

Applying the converse of distributive property  in above eqaution  then we get new equation

$a^2+b^2= c( f+e)$

Because distributive property  a.(b+c)=a.b+a.c

$a^2+b^2=c^2$

Because $e+f = c^2$.