Question

given: ∠1 and ∠2 are supplementary and ∠3 and ∠2 are supplementary. prove: ∠1≅∠3. use the reasons listed to complete the proof. drag and drop an answer choice into each empty box below, or use keyboard navigation. tab to navigate, space to select, arrow key. definition of congruence substitution subtraction property of equality given. statements reasons m∠1 + m∠2 = 180 m∠3 + m∠2 = 180 m∠1 + m∠2 = m∠3 + m∠2 m∠1 = m∠3 ∠1≅∠3

Explanation:

Step1: Given supplementary angles

$m\angle1 + m\angle2 = 180$ (Given)

Step2: Given supplementary angles

$m\angle3 + m\angle2 = 180$ (Given)

Step3: Substitute equal - values

$m\angle1 + m\angle2 = m\angle3 + m\angle2$ (Substitution)

Step4: Use subtraction property

$m\angle1 = m\angle3$ (Subtraction Property of Equality)

Step5: Define congruence

$\angle1\cong\angle3$ (Definition of Congruence)

Answer:

Statements	Reasons
$m\angle3 + m\angle2 = 180$	Given
$m\angle1 + m\angle2 = m\angle3 + m\angle2$	Substitution
$m\angle1 = m\angle3$	Subtraction Property of Equality
$\angle1\cong\angle3$	Definition of Congruence