Question

vx || su. complete the proof that ∠tw v ≅ ∠utw.
statement reason
1 vx || su given
2 ∠tw v ≅ ∠rts corresponding angles theorem
3 ∠rts ≅ ∠utw
4 ∠tw v ≅ ∠utw

Explanation:

Step1: Identify given parallel lines

Given that $\overrightarrow{VX}\parallel\overrightarrow{SU}$.

Step2: Apply corresponding - angles theorem

$\angle TW V$ and $\angle RTS$ are corresponding angles, so $\angle TW V\cong\angle RTS$ (Corresponding Angles Theorem).

Step3: Recall vertical - angles property

$\angle RTS$ and $\angle UTW$ are vertical angles. Since vertical angles are congruent, $\angle RTS\cong\angle UTW$ (Vertical Angles are Congruent).

Step4: Use transitive property of congruence

Since $\angle TW V\cong\angle RTS$ and $\angle RTS\cong\angle UTW$, by the transitive property of congruence, $\angle TW V\cong\angle UTW$.

Answer:

1. Reason: Vertical Angles are Congruent; 4. Reason: Transitive Property of Congruence