Question

yz ⊥ xy and vw ⊥ uv. complete the proof that ∠xyz ≅ ∠uvw.

1 yz ⊥ xy given
2 vw ⊥ uv given
3 m∠xyz = 90°
4 m∠uvw = 90°
5 m∠xyz = m∠uvw transitive property of equality
6 ∠xyz ≅ ∠uvw definition of congruence

Explanation:

Step1: Definition of perpendicular lines

If two lines are perpendicular, the angle between them is \(90^{\circ}\). Since \(\overleftrightarrow{YZ}\perp\overleftrightarrow{XY}\), by the definition of perpendicular lines, \(m\angle XYZ = 90^{\circ}\).

Step2: Definition of perpendicular lines

Similarly, because \(\overleftrightarrow{VW}\perp\overleftrightarrow{UV}\), by the definition of perpendicular lines, \(m\angle UVW=90^{\circ}\).

Answer:

For statement 3, the reason is "Definition of perpendicular lines". For statement 4, the reason is also "Definition of perpendicular lines".