Question

Complete the proof that

Answer 1

Answer:

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

Step-by-step 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