Question

vx || su. complete the proof that ∠utw ≅ ∠twv.

statement
1 vx || su
2 ∠twv ≅ ∠rts
3 ∠rts ≅ ∠utw
4

reason
given
corresponding angles theorem
vertical angle theorem

Explanation:

Step1: Use the transitive property of congruence

If \( \angle TWV\cong\angle RTS\) (from step 2) and \( \angle RTS\cong\angle UTW\) (from step 3), then by the transitive property of congruence (if \(a = b\) and \(b = c\), then \(a = c\)), we can say \( \angle UTW\cong\angle TWV\).

Answer:

\(\angle UTW\cong\angle TWV\) (by the transitive property of congruence)