Question

sv bisects ∠tsu and st ≅ su. complete the proof that tv ≅ uv.

1 sv bisects ∠tsu given
2 st ≅ su given
3 ∠tsv ≅ ∠usv definition of angle bisector
4 sv ≅ sv reflexive property of congruence
5 △stv ≅ △suv sas
6 tv ≅ uv

Explanation:

Step1: Identify given info

$\overrightarrow{SV}$ bisects $\angle TSU$, $\overline{ST} \cong \overline{SU}$ (given)

Step2: Angle bisector definition

$\angle TSV \cong \angle USV$ (angle bisector splits angle into 2 ≅ angles)

Step3: Reflexive property

$\overline{SV} \cong \overline{SV}$ (a segment ≅ itself)

Step4: SAS congruence rule

$\triangle STV \cong \triangle SUV$ (SAS: 2 sides + included angle ≅)

Step5: Corresponding parts of ≅ triangles

$\overline{TV} \cong \overline{UV}$ (CPCTC)

Answer:

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)