Question

→tu ⊥ →uv and →qr ⊥ →rs. complete the proof that ∠tuv ≅ ∠qrs.

statement	reason
2. →qr ⊥ →rs	given
3. m∠tuv = 90°	definition of perpendicular lines
4. m∠qrs = 90°	definition of perpendicular lines
5. m∠tuv = m∠qrs	transitive property of equality
6. ∠tuv ≅ ∠qrs	reason to determine

Explanation:

Step1: Recall the definition of congruent angles

Angles are congruent if their measures are equal.

Step2: Apply the definition to the given angles

We know from step 5 that \( m\angle TUV = m\angle QRS \). By the definition of congruent angles (if two angles have equal measures, then the angles are congruent), we can conclude that \( \angle TUV\cong\angle QRS \).

Answer:

If two angles have equal measures, then the angles are congruent (or Definition of congruent angles)