Question

sv bisects ∠tsu and su ≅ st. complete the proof that △suv ≅ △stv.
statement
1 sv bisects ∠tsu
2 su ≅ st
3 ∠tsv ≅ ∠usv
4 sv ≅ sv
5
reason
given
given
definition of angle bisector
reflexive property of congruence

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

The SAS congruence criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Step2: Identify the sides and included angle for \(\triangle SUV\) and \(\triangle STV\)

We are given that \(\overline{SU}\cong\overline{ST}\) (side), \(\angle TSV\cong\angle USV\) (angle) and \(\overline{SV}\cong\overline{SV}\) (side).

Answer:

\(\triangle SUV\cong\triangle STV\) (by the SAS (Side - Angle - Side) congruence criterion)