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Which statements and reason complete steps 3 , 4 and 6 of the proof ?

Which statements and reason complete steps 3 , 4 and 6 of the proof ?-example-1

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Pythagoras theorem

Statement 1:

ΔABC ≅ ΔCBD ≅ ΔACD

Reason: Given

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Statement 2:

b/c = y/b; a/x = x/a

Reason: corresponding sides of similar triangles are proportional

(we want to have to have in the next statement that b² = cy; a² = cx

and proportionality is usually represented as fractions, if we observe the figure, the fractions of this statement correspond to the division of similar sides of the triangles)

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Statement 3:

b² = cy; a² = cx

Reason: cross product property

(if we multiply both sides of b/c = y/b by b, we obtain b² = cy, and if we do the same for a/x = x/a we obtain a² = cx, since we are multiplying, it is called product, then, the option that best fit this field is cross product property)

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Statement 4:

a² + b² = cx + cy

Reason: addition property of equality

(we want to prove that a² + b² = c², from the previous statement we can add both equalities so we obtain a² + b² , which is nearer to the conclusion we want to prove)

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Statement 5:

a² + b² = c(x + y)

Reason: factor

(we find the common factor of cx and cy, it is c, then cx + cy = c(x + y))

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Statement 6:

c = x + y

Reason: Segment addition postulate

(we almost have the conclusion in the previous statement except for the (x + y) of the right part of the equality, since in the figure we observe that c = x + y, then we can use it to replace (x + y))

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Statement 7:

a² + b² = c²

Reason: substitution

(we substitute c by (x + y) of the statement 5)

Which statements and reason complete steps 3 , 4 and 6 of the proof ?-example-1
Which statements and reason complete steps 3 , 4 and 6 of the proof ?-example-2
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