Question

sv bisects ∠tvx and ∠usw. complete the proof that overline{sw} ≅ overline{su}.

1 sv bisects ∠tvx given
2 sv bisects ∠usw given
3 ∠wvx ≅ ∠tvu
4 ∠svx ≅ ∠svt
5 ∠vsw ≅ ∠usv definition of angle bisector
6 m∠svw = m∠svx + m∠wvx additive property of angle measure
7 m∠svu = m∠svt + m∠tvu
8 m∠svw = m∠svt + m∠tvu substitution
9 m∠svu = m∠svw transitive property of equality
10 overline{sv} ≅ overline{sv} reflexive property of congruence
11 △svw ≅ △svu asa
12 overline{sw} ≅ overline{su} cpctc

Explanation:

Step1: Reason for ∠WVX ≅ ∠TVU

Vertical angles are congruent.

Step2: Reason for ∠SVX ≅ ∠SVT

Definition of angle bisector (since \(\overleftrightarrow{SV}\) bisects \(\angle TVX\)).

Step3: Reason for \(m\angle SVU=m\angle SVT + m\angle TVU\)

Additive Property of Angle Measure.

Answer:

1. Vertical Angles Theorem; 4. Definition of angle bisector; 7. Additive Property of Angle Measure.