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.

Answer 1

The latest sentence of proof by using the triangle congruence method we can conclude that f+e=c, $a^{2} + b^{2} = c^{2}$.

Given that ΔABC and ΔCBD are right triangles

Therefore, one angle of both triangle is of 90°

So, ∠B is same in both triangles. Hence, by suing the Angle-Angle theorem rule we can conclude that both ΔABC and ΔCBD are similar.

Consequently, ∠A is same in both triangles. Hence, by suing the Angle-Angle theorem rule we can conclude that both ΔABC and ΔCBD are similar.

Similarly, When two triangles are similar then their corresponding angles are equal and their corresponding sides are also equal.

Therefore , the two proportions can be rewritten as

a² = cf ( equation 1 )

b² = ce ( equation 2 )

By adding b² on both side of equation 1 then we can write equation 1 as

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

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

Because b² and ce are equal and substitute on the right side of equation 1

Using the converse of distributive property  in above equation then we get a new equation. That is,

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

Because distributive property is a(b+c)=a(b+ac)

a² + b² = c²

Because e + f = c²

To learn more about triangle congruency: brainly.com/question/1675117

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