Question

complete the proof that ∠qur ≅ ∠sut.
diagram: lines intersecting at u, with points s (up), q (down) on one line; r (left), t (right) on another line

statement	reason
2. ( mangle rus + mangle sut = 180^circ )	angles forming a linear pair sum to ( 180^circ )
3. ( mangle qur + mangle rus = mangle rus + mangle sut )	transitive property of equality
4. ( mangle qur = mangle sut )	properties of addition, subtraction, multiplication, and division
5. ( angle qur cong angle sut )	blank for reason

Explanation:

Step1: Recall the definition of congruent angles

If two angles have equal measures, then they are congruent. This is the definition of congruent angles.

Step2: Apply the definition to the given angles

We know from step 4 that \( m\angle QUR = m\angle SUT \). By the definition of congruent angles (if \( m\angle A=m\angle B \), then \( \angle A\cong\angle B \)), we can conclude that \( \angle QUR\cong\angle SUT \).

Answer:

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