Question

∠4 ≅ ∠1
prove
∠4 ≅ ∠3
statement

1. ∠1 and ∠2 are complementary
2. ∠3 and ∠2 are complementary
3. ∠1 ≅ ∠3
4. ∠4 ≅ ∠1
5. ∠4 ≅ ∠3

reason

1. given
2. given
3. ?
4. given
5. transitive property

Explanation:

Step1: Recall the definition of complementary angles

Complementary angles add up to \(90^{\circ}\). So, \(\angle1+\angle2 = 90^{\circ}\) and \(\angle3+\angle2=90^{\circ}\).

Step2: Use the congruent - complements theorem

If two angles are complementary to the same angle, then they are congruent. Since \(\angle1\) and \(\angle3\) are both complementary to \(\angle2\), \(\angle1\cong\angle3\).

Answer:

Congruent - Complements Theorem