Question

Complete the proof that

Answer 1

The two column proof is presented as follows;

Statement
`{}` Reason

ΔSCW ≅ ΔTUW
`{}` Given

`\overline {SV}` ≅
`\overline {TU}`
`{}` CPCTC

`\overline {SW}` ≅
`\overline {TW}`
`{}` CPCTC

`\overline {WV}` ≅
`\overline {UW}`
`{}` CPCTC

∠SVW ≅ ∠TUW
`{}` CPCTC

SU = SW + UV
`{}` Additive property of Length

TU = TW + VW
`{}` Additive property of Length

SU = TW + VW
`{}` Substitution

SU = TV
`{}`
`{}` Transitive property

ΔSTV ≅ ΔTSU
`{}` SAS

∠TSV ≅ ∠STU
`{}` CPCTC

Explanation:

The two column proof is presented as follows;

Statement
`{}` Reason

ΔSCW ≅ ΔTUW
`{}` Given

`\overline {SV}` ≅
`\overline {TU}`
`{}` Congruent Parts of Congruent Triangles are Congruent

`\overline {SW}` ≅
`\overline {TW}`
`{}` Congruent Parts of Congruent Triangles are Congruent

`\overline {UV}` ≅
`\overline {VW}`
`{}` Congruent Parts of Congruent Triangles are Congruent

∠SVW ≅ ∠TUW
`{}`Congruent Parts of Congruent Triangles are Congruent

SU = SW + UV
`{}` Additive property of Length

TU = TW + VW
`{}` Additive property of Length

SU = TW + VW
`{}` Substitution

SU = TV
`{}` Transitive property

ΔSTV ≅ ΔTSU
`{}` Side-Angle-Side rule of congruency

∠TSV ≅ ∠STU
`{}` Congruent Parts of Congruent Triangles are Congruent