Answer:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. ∠V ≅ ∠Y [tex]{}[/tex] Given
2. [tex]\overline {WZ}[/tex] bisects ∠VWY [tex]{}[/tex] Given
3. ∠VWZ = ∠YWZ [tex]{}[/tex] Definition of bisection of angle
4. [tex]\overline {WZ}[/tex] ≅ [tex]\overline {ZW}[/tex] [tex]{}[/tex] Reflexive property
5. ΔWVZ ≅ ΔWYZ [tex]{}[/tex] Angle-Angle-Side congruency postulate
6. [tex]\overline {VZ}[/tex] ≅ [tex]\overline {YZ}[/tex] [tex]{}[/tex] CPCTC postulate
Step-by-step explanation:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. ∠V ≅ ∠Y [tex]{}[/tex] Given
2. [tex]\overline {WZ}[/tex] bisects ∠VWY [tex]{}[/tex] Given
3. Given that ∠VWY is bisected by [tex]\overline {WZ}[/tex], therefore ∠VWY is split into two equal angles, ∠VWZ and ∠YWZ, from which we have ∠VWZ = ∠YWZ [tex]{}[/tex] by the definition of bisection of angle ∠WXY by [tex]\overline{WZ}[/tex]
4. By reflexive property, a line is congruent to itself, therefore, [tex]\overline {WZ}[/tex] ≅ [tex]\overline {ZW}[/tex]
5. Given that two adjacent angles and a side adjacent to the two angles in ΔWVZ are congruent to the corresponding two adjacent angles and adjacent side in ΔWYZ, ΔWVZ is congruent to ΔWYZ by the Angle-Angle-Side (AAS) congruency postulate
6. Given that ΔWVZ ≅ ΔWYZ, and side [tex]\overline {VZ}[/tex] of ΔWVZ is the corresponding side to side [tex]\overline {YZ}[/tex] of ΔWYZ, therefore, [tex]\overline {VZ}[/tex] is congruent to [tex]\overline {YZ}[/tex] by the Congruent Parts of Congruent Triangle are Congruent (CPCTC) postulate.
