The correct answer is. Proportional.
2. ce
3. Segment Addition Postulate.
By the angle-angle similarity postulate, △YXZ∼△YZQ, and △YXZ∼△ZXQ.
The corresponding sides of two similar triangles are proportional.
What is the proportional side of a similar triangle?
Since similar triangles have proportional sides, therefore
[tex]\frac{a}{c}=\frac{f}{a}[/tex] and [tex]\frac{b}{c}=\frac{b}{e}[/tex]
Solving the equation for a² and b² gives
[tex]a^2=cf[/tex] and [tex]b^2=ce[/tex]
The value of a² is cf and the value b² is ce.
Adding these together gives
[tex]a^2+b^2=cf+ce[/tex]
Factoring out the common segment gives
[tex]a^2+b^2=c(f+e)[/tex]
From the given figure it is clear that
[tex]c=f+e[/tex]
(Segment Addition Postulate)
Using the Segment Addition Postulate, we get
[tex]a^2+b^2=c(c)[/tex]
On simplification, we get
[tex]a^2+b^2=c^2[/tex]
Therefore the required answers are 1. Proportional, 2. ce, 3. Segment Addition Postulate.
To learn more about the Pythagorean theorem visit:
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