Question

∠t and ∠s are supplementary and ∠u and ∠s are supplementary. complete the proof that ∠t ≅ ∠u.

1 ∠t and ∠s are supplementary given
2 ∠u and ∠s are supplementary given
3 m∠t + m∠s = 180° definition of supplementary angles
4 m∠u + m∠s = 180°
5 m∠t + m∠s = m∠u + m∠s transitive property of equality
6 m∠t = m∠u
7 ∠t ≅ ∠u definition of congruence

Explanation:

Step1: Determine the reason for statement 4

Since $\angle U$ and $\angle S$ are supplementary (given in statement 2), by the definition of supplementary angles (if two angles are supplementary, the sum of their measures is $180^{\circ}$), the reason for statement 4 is "Definition of supplementary angles".

Step2: Determine the reason for statement 6

We have $m\angle T + m\angle S=m\angle U + m\angle S$ (statement 5). Subtracting $m\angle S$ from both sides of the equation $m\angle T + m\angle S=m\angle U + m\angle S$ (using the Subtraction Property of Equality: if $a + c=b + c$, then $a=b$ where $a = m\angle T$, $b = m\angle U$ and $c=m\angle S$), the reason for statement 6 is "Subtraction Property of Equality".

Answer:

Statement	Reason
2	$\angle U$ and $\angle S$ are supplementary	Given
3	$m\angle T + m\angle S = 180^{\circ}$	Definition of supplementary angles
4	$m\angle U + m\angle S = 180^{\circ}$	Definition of supplementary angles
5	$m\angle T + m\angle S = m\angle U + m\angle S$	Transitive Property of Equality
6	$m\angle T = m\angle U$	Subtraction Property of Equality
7	$\angle T\cong\angle U$	Definition of congruence