Question

complete the proof that ∠txu ≅ ∠tux.
statement reason
1 $overleftrightarrow{ux} parallel overleftrightarrow{vw}$ given
2 ∠uvw ≅ ∠w given
3 ∠w ≅ ∠txu corresponding angles theorem
4 ∠uvw ≅ ∠tux corresponding angles theorem
5 ∠uvw ≅ ∠txu transitive property of congruence
6 ∠txu ≅ ∠tux

Explanation:

Step1: Recall transitive property

We know from steps 2, 3 and 5 that $\angle UVW\cong\angle W$, $\angle W\cong\angle TXU$ and $\angle UVW\cong\angle TXU$. Also from step 4, $\angle UVW\cong\angle TUX$.

Step2: Apply transitive property

Since $\angle TXU\cong\angle UVW$ (from step 5) and $\angle UVW\cong\angle TUX$ (from step 4), by the transitive - property of congruence, we can conclude that $\angle TXU\cong\angle TUX$.

Answer:

Transitive Property of Congruence