Question

wxyz is a trapezoid with \\( \overline { wx } \cong \overline { yz } \\).
what is the length of \\( \overline { xy } \\)?
3 units
4 units
5 units
6 units

Explanation:

Step1: Use the property of congruent sides

Since \( \overline{WX}\cong\overline{YZ}\), we have \(2a - 2=a + 1\).

Step2: Solve the equation for \(a\)

Subtract \(a\) from both sides: \(2a-a-2=a - a+ 1\), so \(a-2 = 1\).
Add \(2\) to both sides: \(a-2 + 2=1 + 2\), then \(a = 3\).

Step3: Find the length of \(XY\)

Substitute \(a = 3\) into the expression for \(XY\) (which is \(3a-4\)).
\(XY=3a-4=3\times3 - 4=9 - 4=5\).

Answer:

5 units