Question

if st = z and pr = z - 9, what is the value of z?
t
p
q
r
s
z = \boxed{}

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment (PR) of a triangle is half the length of the parallel side (ST). So, \(PR=\frac{1}{2}ST\).

Step2: Substitute the given expressions

Given \(ST = z\) and \(PR=z - 9\), substitute into the equation \(z-9=\frac{1}{2}z\).

Step3: Solve the equation

Subtract \(\frac{1}{2}z\) from both sides: \(z-\frac{1}{2}z-9 = 0\), which simplifies to \(\frac{1}{2}z-9=0\). Then add 9 to both sides: \(\frac{1}{2}z=9\). Multiply both sides by 2: \(z = 18\).

Answer:

\(18\)