Answer:
Because f+e=c, [tex]a^2+b^2=c^2[/tex].
Step-by-step explanation:
Given [tex]\triangle ABC[/tex] and [tex]\triangle CBD[/tex] are right triangles.
To prove that [tex]a^2+b^2=c^2[/tex]
Because [tex]\triangle ABC\; and \;\triangle CBD[/tex]  both have a right angle. It means  one angle of both triangle is of[tex]90^{\circ}[/tex].
And tha angle B is same in both triangles .Therefore, triangles must be similar by AA similarity.
Similarly ,  [tex]\triangle ABC[/tex] and [tex]\triangle  CBD[/tex]  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
[tex]a^2=cf[/tex] Â ( I equation )
[tex]b^2=ce[/tex] ( II equation )
Adding [tex]b^2[/tex] on both side of I equation  then we  can write equation I as
[tex]a^2+b^2=b^2+cf[/tex]
[tex]a^2+b^2= ce+cf[/tex]
Because [tex]b^2[/tex] 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
[tex]a^2+b^2= c( f+e)[/tex]
Because distributive property  a.(b+c)=a.b+a.c
[tex]a^2+b^2=c^2[/tex]
Because [tex]e+f = c^2[/tex].
