Question

1. given: \\( \triangle svt \cong \triangle swt \\).

prove: \\( \overline { st } \\) bisects \\( \angle vsw \\).

statements	reasons
2.	2. corresponding parts of congruent
3. \\( \overline { st } \\) bisects \\( \angle vsw \\).	3. figures are congruent.

1. bank. you may use each statement once, not at all, or more than once.

def. of angle bisector	\\( \overline { a d } \cong \overline { c d } \\)
\\( \angle t s v \cong \angle t s w \\)	transitive property of congruence
quadrilateral \\( a b c d \cong \\) quadrilateral \\( e f g h \\)

Explanation:

Step1: Identify the given information

We are given that \(\triangle SVT\cong\triangle SWT\).

Step2: Use the property of congruent triangles

When two triangles are congruent, their corresponding parts are congruent. So, \(\angle VST\cong\angle WST\) (by the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) property).

Step3: Apply the definition of an angle bisector

An angle bisector is a ray that divides an angle into two congruent angles. Since \(\angle VST\cong\angle WST\), \(\overline{ST}\) bisects \(\angle VSW\) (by the definition of an angle bisector).

Answer:

1. Given
2. Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
3. Def. of Angle Bisector