Question

st ⊥ tu and qr ⊥ pq. complete the proof that ∠stu ≅ ∠pqr.
statement\treason
1 st ⊥ tu\tgiven
2 qr ⊥ pq\tgiven
3 m∠stu = 90°\tdefinition of perpendicular lines
4 m∠pqr = 90°\tdefinition of perpendicular lines
5 m∠stu = m∠pqr\ttransitive property of equality
6 \t

Explanation:

Step1: Recall angle - congruence definition

If two angles have the same measure, they are congruent.

Step2: Use previous statements

Since \(m\angle STU=m\angle PQR = 90^{\circ}\) (from statements 3, 4, 5), by the definition of congruent angles (angles with equal measures are congruent).

Answer:

\(\angle STU\cong\angle PQR\); Definition of congruent angles