Question

Complete the flow proof​

Answer 1

The two column proof is presented as follows;

Statement
`{}` Reason

1. ∠V ≅ ∠Y
`{}` Given

2.
`\overline {WZ}` bisects ∠VWY
`{}` Given

3. ∠VWZ = ∠YWZ
`{}` Definition of bisection of angle

4.
`\overline {WZ}` ≅
`\overline {ZW}`
`{}` Reflexive property

5. ΔWVZ ≅ ΔWYZ
`{}` Angle-Angle-Side congruency postulate

6.
`\overline {VZ}` ≅
`\overline {YZ}`
`{}` CPCTC postulate

Explanation:

The two column proof is presented as follows;

Statement
`{}` Reason

1. ∠V ≅ ∠Y
`{}` Given

2.
`\overline {WZ}` bisects ∠VWY
`{}` Given

3. Given that ∠VWY is bisected by
`\overline {WZ}`, therefore ∠VWY is split into two equal angles, ∠VWZ and ∠YWZ, from which we have ∠VWZ = ∠YWZ
`{}` by the definition of bisection of angle ∠WXY by
`\overline{WZ}`

4. By reflexive property, a line is congruent to itself, therefore,
`\overline {WZ}` ≅
`\overline {ZW}`

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
`\overline {VZ}` of ΔWVZ is the corresponding side to side
`\overline {YZ}` of ΔWYZ, therefore,
`\overline {VZ}` is congruent to
`\overline {YZ}` by the Congruent Parts of Congruent Triangle are Congruent (CPCTC) postulate.