Question

Triangle XYZ is a right triangle with ZQ¯¯¯¯¯⊥XY¯¯¯¯¯¯ .

Answer 1

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

$\frac{a}{c}=\frac{f}{a}$ and $\frac{b}{c}=\frac{b}{e}$

Solving the equation for a² and b² gives

$a^2=cf$ and $b^2=ce$

The value of a² is cf and the value b² is ce.

Adding these together gives

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

Factoring out the common segment gives

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

From the given figure it is clear that

$c=f+e$

        (Segment Addition Postulate)

Using the Segment Addition Postulate, we get

$a^2+b^2=c(c)$

On simplification, we get

$a^2+b^2=c^2$

Therefore the required answers are 1. Proportional, 2. ce, 3. Segment Addition Postulate.

To learn more about the Pythagorean theorem visit:

brainly.com/question/343682

#SPJ1