Question

∠swt ≅ ∠twu. complete the proof that \\(overleftrightarrow{tv} \perp overleftrightarrow{su}\\).

diagram: two intersecting lines at point w, labeled with arrows: s (top-left), t (top-right), v (bottom-left), u (bottom-right)

statement	reason
2 \\(m\angle swt + m\angle twu = 180^\circ\\)	angles forming a linear pair sum to \\(180^\circ\\)
3 \\(m\angle swt + m\angle swt = 180^\circ\\)	substitution
4 \\(m\angle swt = 90^\circ\\)	properties of addition, subtraction, multiplication, and division
5 \\(\\)	\\(\\)

Explanation:

Step1: Recall the definition of perpendicular lines

Two lines are perpendicular if the angle between them is \(90^\circ\). We know that \(\angle SWT = 90^\circ\) from step 4, and \(\angle SWT\) is the angle between \(\overleftrightarrow{TV}\) and \(\overleftrightarrow{SU}\) at their intersection \(W\).

Step2: State the conclusion based on the definition

Since \(m\angle SWT = 90^\circ\), by the definition of perpendicular lines, \(\overleftrightarrow{TV} \perp \overleftrightarrow{SU}\).

Answer:

Statement: \(\overleftrightarrow{TV} \perp \overleftrightarrow{SU}\)
Reason: If two lines intersect to form a \(90^\circ\) angle, then they are perpendicular.