Question

1. given: ∠1 and ∠2 are complementary and ∠3 and ∠2 are complementary. prove: ∠1 ≅ ∠3 use the reasons listed to complete the proof. definition of congruence, substitution, subtraction property of equality, given statements reasons m∠1 + m∠2 = 90 m∠3 + m∠2 = 90 m∠1 + m∠2 = m∠3 + m∠2 m∠1 = m∠3 ∠1 ≅ ∠3

Explanation:

Step1: State given facts

Given

Step2: State given facts

Given

Step3: Substitute equal - values

Substitution

Step4: Apply subtraction property

Subtraction Property of Equality

Step5: Use congruence definition

Definition of Congruence

Answer:

Statements	Reasons
$m\angle3 + m\angle2 = 90$	Given
$m\angle1 + m\angle2=m\angle3 + m\angle2$	Substitution
$m\angle1=m\angle3$	Subtraction Property of Equality
$\angle1\cong\angle3$	Definition of Congruence