Question

given: ∠1 and ∠2 are supplements, ∠3 and ∠4 are supplements, and ∠1≅∠4. prove: ∠2≅∠3. assemble the proof by dragging tiles to the statements and reasons columns.

Explanation:

Step1: Given supplementary - angle property

Since $\angle1$ and $\angle2$ are supplements, $m\angle1 + m\angle2=180$. Also, since $\angle3$ and $\angle4$ are supplements, $m\angle3 + m\angle4 = 180$.

Step2: Substitution

Given $\angle1\cong\angle4$, so $m\angle1=m\angle4$. Substitute $m\angle1$ for $m\angle4$ in $m\angle3 + m\angle4 = 180$, we get $m\angle3 + m\angle1=180$.

Step3: Transitive property

We have $m\angle1 + m\angle2=180$ and $m\angle3 + m\angle1=180$. By the transitive property of equality (if $a + b=c$ and $d + b=c$, then $a=d$), we can subtract $m\angle1$ from both equations. So $m\angle2=m\angle3$, which means $\angle2\cong\angle3$.

Answer:

Statements	Reasons
$m\angle3 + m\angle4 = 180$	$\angle3$ and $\angle4$ are supp.
$\angle1\cong\angle4$	Given
$m\angle1=m\angle4$	Definition of congruent angles
$m\angle1 + m\angle2=m\angle3 + m\angle1$	Substitution ($m\angle4$ replaced by $m\angle1$ in $m\angle3 + m\angle4 = 180$)
$m\angle2=m\angle3$	Subtraction property of equality (subtract $m\angle1$ from both sides)
$\angle2\cong\angle3$	Definition of congruent angles