Question

fg ⊥ ef and hi ⊥ ij. complete the proof that ∠efg ≅ ∠hij.
statement\treason
1 fg ⊥ ef
2 hi ⊥ ij
3 m∠efg = 90°
4 m∠hij = 90°
5 m∠efg = m∠hij
6 ∠efg ≅ ∠hij

Explanation:

Step1: Given information

Given

Step2: Given information

Given

Step3: Definition of perpendicular lines

If two lines are perpendicular, the angle between them is 90°.

Step4: Definition of perpendicular lines

If two lines are perpendicular, the angle between them is 90°.

Step5: Transitive property of equality

Since \(m\angle EFG = 90^{\circ}\) and \(m\angle HIJ=90^{\circ}\), then \(m\angle EFG=m\angle HIJ\).

Step6: Definition of congruent angles

If the measures of two angles are equal, the angles are congruent.

Answer:

1. Given
2. Given
3. Definition of perpendicular lines
4. Definition of perpendicular lines
5. Transitive property of equality
6. Definition of congruent angles