Question

complete the paragraph proof.
given: ∠1 and ∠2 are complementary and ∠2 and ∠3 are complementary.
prove: ∠1≅∠3
it is 6. ____________ that ∠1 and ∠2 are complementary and ∠2 and ∠3 are complementary. by the definition of 7. __________________________, m∠1 + m∠2 = 90° and m∠2 + m∠3 = 90°. by the 8. __________________ property, m∠1 + m∠2 = m∠2 + m∠3.
then, m∠1 = 9. ____________ by the subtraction property. therefore, ∠1≅∠3 by the 10. __________________.

Explanation:

Step1: State given fact

Given

Step2: Recall complementary - angles definition

Complementary angles

Step3: Use transitive property of equality

Transitive

Step4: Apply subtraction property

$m\angle3$

Step5: Recall congruent - angles definition

Definition of congruent angles

Answer:

1. Given
2. Complementary angles
3. Transitive
4. $m\angle3$
5. Definition of congruent angles