Question

fg ⊥ gh and ij ⊥ jk. complete the proof that ∠fgh ≅ ∠ijk.
1 fg ⊥ gh
2 ij ⊥ jk
3 m∠fgh = 90°
4 m∠ijk = 90°
5 m∠fgh = m∠ijk
6 ∠fgh ≅ ∠ijk

Explanation:

Step1: Given

Statement 1: \(\overleftrightarrow{FG}\perp\overleftrightarrow{GH}\) is given.

Step2: Given

Statement 2: \(\overleftrightarrow{IJ}\perp\overleftrightarrow{JK}\) is given.

Step3: Definition of perpendicular lines

If two lines are perpendicular, the measure of the angle formed is \(90^{\circ}\). So, \(m\angle FGH = 90^{\circ}\) (from \(\overleftrightarrow{FG}\perp\overleftrightarrow{GH}\)).

Step4: Definition of perpendicular lines

Similarly, \(m\angle IJK=90^{\circ}\) (from \(\overleftrightarrow{IJ}\perp\overleftrightarrow{JK}\)).

Step5: Transitive property of equality

Since \(m\angle FGH = 90^{\circ}\) and \(m\angle IJK = 90^{\circ}\), by transitive property \(m\angle FGH=m\angle IJK\).

Step6: Definition of congruent angles

If the measures of two angles are equal, then the angles are congruent. So, \(\angle FGH\cong\angle IJK\).

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