Question

1. \\(\frac{ab}{zy} = \frac{bc}{yx} = 2\\)
2. \\(\angle b\\) and \\(\angle y\\) are right angles.

3.?
4.?
which two statements are missing in steps 3 and 4?
\\(\angle x \cong \angle c\\)
\\(\triangle abc \sim \triangle zyx\\) by the sas similarity theorem.
\\(\angle b \cong \angle y\\)
\\(\triangle abc \sim \triangle zyx\\) by the sas similarity theorem.
\\(\frac{ac}{} = 2\\)

Explanation:

To prove triangle similarity using SAS similarity, we need two proportional sides and the included angle congruent. Step 1 gives proportional sides $\frac{AB}{ZY} = \frac{BC}{YX} = 2$. Step 2 states $\angle B$ and $\angle Y$ are right angles, so Step 3 should confirm $\angle B \cong \angle Y$ (right angles are congruent). Step 4 then concludes similarity via SAS similarity theorem.

Answer:

$\angle B \cong \angle Y$, $\triangle ABC \sim \triangle ZYX$ by the SAS similarity theorem.