Questions: W X is perpendicular to V W and S T is perpendicular to T U. Complete the proof that angle S T U is congruent to angle V W X. - Statement - Reason 1. W X is perpendicular to V W - 2. S T is perpendicular to T U - 3. m angle V W X=90° - 4. m angle S T U=90° - 5. m angle V W X=m angle S T U - 6. angle S T U is congruent to angle V W X -

Solution Steps

To complete the proof that \(\angle STU \cong \angle VWX\), we need to show that both angles are right angles and have the same measure. The given statements indicate that both pairs of lines are perpendicular, which implies that the angles formed are right angles. Therefore, both \(\angle VWX\) and \(\angle STU\) measure \(90^\circ\). Since they have the same measure, they are congruent.

We are given that \(\overleftrightarrow{WX} \perp \overleftrightarrow{VW}\) and \(\overleftrightarrow{ST} \perp \overleftrightarrow{TU}\). This implies that both \(\angle VWX\) and \(\angle STU\) are right angles.

Since both angles are right angles, we have: \[ m \angle VWX = 90^\circ \] \[ m \angle STU = 90^\circ \]

Since \( m \angle VWX = m \angle STU = 90^\circ \), it follows that: \[ m \angle VWX = m \angle STU \]

Since the measures of \(\angle VWX\) and \(\angle STU\) are equal, the angles are congruent: \[ \angle STU \cong \angle VWX \]

Final Answer