Question

complete the proof that ∠qur ≅ ∠sut.
statement reason
1 m∠qur + m∠rus = 180°
2 m∠rus + m∠sut = 180°
3 m∠qur + m∠rus = m∠rus + m∠sut
4 m∠qur = m∠sut
5 ∠qur ≅ ∠sut

Explanation:

Step1: Definition of linear - pair

$\angle QUR$ and $\angle RUS$ form a linear - pair, so $m\angle QUR + m\angle RUS=180^{\circ}$.

Step2: Definition of linear - pair

$\angle RUS$ and $\angle SUT$ form a linear - pair, so $m\angle RUS + m\angle SUT = 180^{\circ}$.

Step3: Transitive property of equality

Since $m\angle QUR + m\angle RUS=180^{\circ}$ and $m\angle RUS + m\angle SUT = 180^{\circ}$, then $m\angle QUR + m\angle RUS=m\angle RUS + m\angle SUT$.

Step4: Subtraction property of equality

Subtract $m\angle RUS$ from both sides of the equation $m\angle QUR + m\angle RUS=m\angle RUS + m\angle SUT$, we get $m\angle QUR=m\angle SUT$.

Step5: Definition of congruent angles

If $m\angle QUR=m\angle SUT$, then $\angle QUR\cong\angle SUT$ by the definition of congruent angles (angles with equal measures are congruent).

Answer:

1. Reason: Linear - pair postulate
2. Reason: Linear - pair postulate
3. Reason: Transitive property of equality
4. Reason: Subtraction property of equality
5. Reason: Definition of congruent angles