brainliest if

use the drop-down menus to complete the proof of the pythagorean theorem.

by the angle-angle similarity postulate, △yxz∼△yzq and △yxz∼△zxq. since similar triangles have
sides, ac=fa and bc=eb . solving the equation for a² and b² gives a2=cf and b2= . adding these together gives a2+b2=cf+ce. factoring out the common segment gives a2+b2=c(f+e). using gives a2+b2=c(c), which simplifies to a2+b2=c2 .

1. Proportional.

2. ce

3. Segment Addition Postulate.

Step-by-step explanation:

By the angle-angle similarity postulate, △YXZ∼△YZQ and △YXZ∼△ZXQ.

The corresponding sides of two similar triangles are proportional.

Since similar triangles have  proportional sides, therefore

and

Solving the equation for a² and b² gives

and

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

Adding these together gives

Factoring out the common segment gives

From the given figure it is clear that

        (Segment Addition Postulate)

Using segment Addition Postulate, we get

On simplification, we get

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