Question

if uv = z and wy = z - 44, what is the value of z?
(image of a geometric figure with points v, w, x, y, u, and markings indicating congruent segments)
z =

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment of a triangle (a segment connecting the mid - points of two sides of a triangle) is half the length of the third side. Here, \(WY\) is the mid - segment of \(\triangle VXU\) and \(UV\) is the third side. So, \(WY=\frac{1}{2}UV\).

Step2: Substitute the given expressions

Given \(UV = z\) and \(WY=z - 44\), substituting into the equation \(WY=\frac{1}{2}UV\) gives \(z-44=\frac{1}{2}z\).

Step3: Solve the equation for \(z\)

Subtract \(\frac{1}{2}z\) from both sides: \(z-\frac{1}{2}z-44 = 0\), which simplifies to \(\frac{1}{2}z-44=0\). Then add 44 to both sides: \(\frac{1}{2}z=44\). Multiply both sides by 2: \(z = 88\).

Answer:

\(88\)