Question

4pts: prove ∠wxu≅∠sut, without using the fact that they are corresponding.

Explanation:

Step1: Use the property of vertical angles

$\angle WXU$ and $\angle SXY$ are vertical angles. So, $\angle WXU\cong\angle SXY$ (Vertical angles are congruent).

Step2: Use the property of parallel lines (assuming $WY\parallel TV$)

If $WY\parallel TV$ and $ZS$ is a transversal, then $\angle SXY\cong\angle SUT$ (Corresponding angles for parallel lines $WY$ and $TV$ cut by transversal $ZS$).

Step3: Use the transitive property of congruence

Since $\angle WXU\cong\angle SXY$ and $\angle SXY\cong\angle SUT$, by the transitive property of congruence (if $a = b$ and $b = c$, then $a = c$ for congruent angles), we have $\angle WXU\cong\angle SUT$.

Answer:

$\angle WXU\cong\angle SUT$ is proved as above.