1) w is the midpoint of $ \overline{st} $ and $ \overline{vt} $ 1) given
2) $ \overline{vw} \cong \overline{vw} $ 2)
3) 3) definition of midpoint
4) $ \angle jvw \cong \angle swt $ 4)
5) $ \triangle jvw \cong \triangle swt $ 5)
\# ssa \# vertical angles are congruent \# sas \# reflexive \# definition of midpoint \# $ \overline{vt} \cong \overline{st} $ \# distributive
\# definition of a linear pair

Question

Accepted Answer

# Explanation:
## Step1: Find reason for $ \overline{VW}\cong\overline{VW} $
Reflexive property (any segment is congruent to itself).
## Step2: Find statement for definition of midpoint
$ \overline{UV}\cong\overline{ST} $ (by definition of mid - point, a mid - point divides a segment into two congruent segments).
## Step3: Find reason for $ \angle UVW\cong\angle SWT $
Vertical angles are congruent.
## Step4: Find reason for $ \triangle UVW\cong\triangle STW $
SAS (Side - Angle - Side) congruence criterion ($ \overline{UV}\cong\overline{ST} $, $ \angle UVW\cong\angle SWT $, $ \overline{VW}\cong\overline{VW} $).

# Answer:
2) Reflexive; 3) $ \overline{UV}\cong\overline{ST} $; 4) Vertical angles are congruent; 5) SAS.

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QUESTION IMAGE

Question

Explanation:

Step1: Find reason for \( \overline{VW}\cong\overline{VW} \)

Step2: Find statement for definition of midpoint

Step3: Find reason for \( \angle UVW\cong\angle SWT \)

Step4: Find reason for \( \triangle UVW\cong\triangle STW \)

Answer: