Question

if st = y + 16 and pr = y, what is pr? pr =

Explanation:

Step1: Use the mid - segment theorem

In a triangle, the mid - segment (a segment connecting the mid - points of two sides of a triangle) is parallel to the third side and half its length. Here, \(PR\) is the mid - segment of \(\triangle QST\) (since \(P\) is the mid - point of \(QT\) and \(R\) is the mid - point of \(QS\)). So, \(PR=\frac{1}{2}ST\).

Step2: Substitute the given expressions

Given \(ST = y + 16\) and \(PR=y\). Substituting into \(PR=\frac{1}{2}ST\), we get \(y=\frac{1}{2}(y + 16)\).

Step3: Solve the equation

Multiply both sides of the equation \(y=\frac{1}{2}(y + 16)\) by \(2\) to get \(2y=y + 16\). Then subtract \(y\) from both sides: \(2y-y=y + 16-y\).

Answer:

\(16\)