Question

given: ∠1 and ∠2 are complementary. ∠1≅∠3, ∠2≅∠4
prove: ∠3 and ∠4 are complementary.
statements

1. ∠1 and ∠2 are complementary.
2. m∠1 + m∠2 = 90°
3. ∠1≅∠3, ∠2≅∠4
4. m∠1 = m∠3, m∠2 = m∠4
5. m∠3 + m∠2 = 90°

reasons

1. ?
2. ?
3. ?
4. ?
5. ?

Explanation:

Step1: Given information

Given

Step2: Definition of complementary angles

If two angles are complementary, the sum of their measures is 90°. So, if ∠1 and ∠2 are complementary, then $m\angle1 + m\angle2=90^{\circ}$

Step3: Given congruent - angle information

Given

Step4: Definition of congruent angles

Congruent angles have equal measures. So, if ∠1≅∠3 and ∠2≅∠4, then $m\angle1 = m\angle3$ and $m\angle2 = m\angle4$

Step5: Substitution property

Substitute $m\angle1$ with $m\angle3$ in the equation $m\angle1 + m\angle2=90^{\circ}$, we get $m\angle3 + m\angle2=90^{\circ}$

Step6: Conclusion

Since $m\angle3 + m\angle4=90^{\circ}$, ∠3 and ∠4 are complementary (by the definition of complementary angles)

Answer:

1. Given
2. Definition of complementary angles
3. Given
4. Definition of congruent angles
5. Substitution property
6. Definition of complementary angles (because $m\angle3 + m\angle4 = 90^{\circ}$)