Question

uv→⊥vw→ and yz→⊥xy→. complete the proof that ∠uvw≅∠xyz.
statement\treason
1 uv→⊥vw→\tgiven
2 yz→⊥xy→\tgiven
3 m∠uvw = 90°\tgiven
4 m∠xyz = 90°\t
5 m∠uvw = m∠xyz\tdefinition of perpendicular lines
6 ∠uvw≅∠xyz\ttransitive property of equality
\tdefinition of congruence

Explanation:

Step1: Recall perpendicular - angle relationship

If two lines are perpendicular, the angle formed by them is 90 degrees. Since $\overleftrightarrow{YZ}\perp\overleftrightarrow{XY}$, by the definition of perpendicular lines, the measure of the angle formed by them, $\angle XYZ$, is 90 degrees.

Step2: Use congruence definition

Congruent angles have equal measures. We have shown that $m\angle UVW = 90^{\circ}$ and $m\angle XYZ=90^{\circ}$, so $m\angle UVW = m\angle XYZ$. By the definition of congruence (if the measures of two angles are equal, the angles are congruent), $\angle UVW\cong\angle XYZ$.

Answer:

1. Definition of perpendicular lines
2. Transitive Property of Equality
3. Definition of congruence