Question

uv ⊥ tu and rs ⊥ qr. complete the proof that ∠qrs ≅ ∠tuv.
statement reason
1 uv ⊥ tu given
2 rs ⊥ qr given
3 m∠tuv = 90° definition of perpendicular lines
4 m∠qrs = 90°
5 m∠tuv = m∠qrs transitive property of equality
6 ∠qrs ≅ ∠tuv definition of congruence

Explanation:

Step1: Recall perpendicular - lines property

Since $\overleftrightarrow{RS}\perp\overleftrightarrow{QR}$, by the definition of perpendicular lines, the angle formed by them is a right - angle.

Step2: Fill in the reason

The reason for $m\angle QRS = 90^{\circ}$ is "Definition of perpendicular lines".

Answer:

Definition of perpendicular lines