complete the proof that $ \angle sru \cong \angle rut $.

1 $ \overleftrightarrow { tv } \parallel \overleftrightarrow { qs } $ given
2 $ \angle rut \cong \angle prq $
3 $ \angle prq \cong \angle sru $ vertical angle theorem
4 $ \angle sru \cong \angle rut $

Question

complete the proof that $ \angle sru \cong \angle rut $.

1 $ \overleftrightarrow { tv } \parallel \overleftrightarrow { qs } $ given
2 $ \angle rut \cong \angle prq $
3 $ \angle prq \cong \angle sru $ vertical angle theorem
4 $ \angle sru \cong \angle rut $

Accepted Answer

# Explanation:
## Step1: Identify given parallel lines
Given $ TV \parallel QS $ (from Statement 1).
## Step2: Corresponding angles for parallel lines
Since $ TV \parallel QS $ and transversal $ PW $ intersects them, $ \angle RUT \cong \angle PRQ $ by Corresponding Angles Theorem (correct reason for Statement 2, replacing "Substitution").
## Step3: Vertical angles are congruent
$ \angle PRQ \cong \angle SRU $ by Vertical Angle Theorem (Statement 3, correct reason).
## Step4: Transitive property of congruence
From $ \angle RUT \cong \angle PRQ $ and $ \angle PRQ \cong \angle SRU $, $ \angle SRU \cong \angle RUT $ by Transitive Property of Congruence.

# Answer:
Transitive Property of Congruence (for Statement 4's reason)
Corresponding Angles Theorem (corrected reason for Statement 2)

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QUESTION IMAGE

Question

Explanation:

Step1: Identify given parallel lines

Step2: Corresponding angles for parallel lines

Step3: Vertical angles are congruent

Step4: Transitive property of congruence

Answer: