Question

st ⊥ tu and vw ⊥ wx. complete the proof that ∠vwx ≅ ∠stu.

1 st ⊥ tu given
2 vw ⊥ wx given
3 m∠stu = 90°
4 m∠vwx = 90° definition of perpendicular lines
5 m∠stu = m∠vwx transitive property of equality
6 ∠vwx ≅ ∠stu

Explanation:

Step1: Determine the reason for \(m\angle STU = 90^{\circ}\)

Since \(\overleftrightarrow{ST}\perp\overleftrightarrow{TU}\), by the definition of perpendicular lines (if two lines are perpendicular, then the measure of the angle formed by them is \(90^{\circ}\)), we have \(m\angle STU = 90^{\circ}\).

Step2: Determine the reason for \(\angle VWX\cong\angle STU\)

We know that if \(m\angle A=m\angle B\), then \(\angle A\cong\angle B\) (by the definition of congruent angles: two angles are congruent if and only if their measures are equal). Here, \(m\angle STU = m\angle VWX\) (from step 5), so \(\angle VWX\cong\angle STU\) by the definition of congruent angles.

Answer:

For statement 3, the reason is "Definition of perpendicular lines". For statement 6, the reason is "Definition of congruent angles".