Question

∠vzw ≅ ∠wzx. complete the proof that $overleftrightarrow{wy} perp overleftrightarrow{vx}$. diagram of lines w, v, x, y intersecting at z

statement	reason
2. ( mangle vzw + mangle wzx = 180^circ )	reason to determine
3. ( mangle vzw + mangle vzw = 180^circ )	substitution
4. ( mangle vzw = 90^circ )	properties of addition, subtraction, multiplication, and division
5. ( overleftrightarrow{wy} perp overleftrightarrow{vx} )	definition of perpendicular lines

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Explanation:

Step1: Identify the angle relationship

Angles \(\angle VZW\) and \(\angle WZX\) are adjacent and form a linear pair (they lie on a straight line \(VX\)), so their measures add up to \(180^\circ\). This is the definition of a linear pair of angles, which states that if two angles form a linear pair, then they are supplementary (their measures sum to \(180^\circ\)).

Step2: Determine the reason for step 2

The reason for \(m\angle VZW + m\angle WZX = 180^\circ\) is that \(\angle VZW\) and \(\angle WZX\) form a linear pair, and linear pairs of angles are supplementary (sum to \(180^\circ\)). So the reason is "Linear Pair Postulate (or Definition of Linear Pair: adjacent angles forming a straight line are supplementary)".

Answer:

The reason for step 2 is "Linear Pair Postulate (or Definition of Linear Pair: adjacent angles forming a straight line are supplementary)".