Question

∠uvz ≅ ∠wyx, \overline{vw} ≅ \overline{yz}, and ∠xwy ≅ ∠uzv. complete the proof that △wxy ≅ △zuv.

Explanation:

Step1: Substitute $YZ$ with $VW$

Since $YZ = VW$ (given $\overline{VW}\cong\overline{YZ}$), and $VZ=YZ + VY$ (Statement 4), we substitute $YZ$ with $VW$. So, $VZ = VW+VY$.

Step2: Use the substitution property

From Statement 5 ($WY = VW + VY$) and Statement 6 ($VZ=VW + VY$), by the substitution property (if $a=b$ and $a = c$, then $b = c$), we can conclude that $WY=VZ$.

Answer:

1. Substitution Property (substitute $YZ$ with $VW$ in $VZ = YZ+VY$ as $YZ = VW$); 7. Substitution Property (substitute $VW + VY$ in $WY = VW + VY$ with $VZ$ as $VZ=VW + VY$)