Question

Which is the last sentence of the proof?

Because f + e = 1, a2 + b2 = c2.
Because f + e = c, a2 + b2 = c2.
Because a2 + b2 = c2, f + e = c.
Because a2 + b2 = c2, f + e = 1.

Given: Right △ABC as shown where CD is an altitude of the triangle
Prove: a2 + b2 = c2

Answer 1

Given: A right triangle ABC in which CD is an altitude of ACB, right angled at C.

To prove: $a^{2}+ b^{2}=c^{2}$

Proof: In Δ AC B and ΔADC

 ∠A is common.

∠C =∠ADC[each being 90°]

Δ AC B ~ ΔADC[AA]

$\frac{AC}{AD}=\frac{BC}{DC}=\frac{AB}{AC}\\\frac{b}{e}=\frac{a}{h}=\frac{c}{b}$→→  [when triangles are similar sides are proportional]

→$b^{2}=ce$...........(1)

Similarly , by proving ΔA CB and Δ C DB similar by AA similarity,

we will get ,$a^{2}=fc$ .............(2)

adding (1) and (2)

$b^{2}+a^{2}=fc+ce$

             = c(f+e)

But, f+e=c,

so,$b^{2}+a^{2}=c^{2}$

So,option 2 which is Because f + e = c,So$b^{2}+a^{2}=c^{2}$