Question

if ( tu = z + 39 ) and ( vx = 2z ), what is the value of ( z )?

Explanation:

Step1: Identify Midsegment Theorem

In a triangle, the midsegment (a segment connecting midpoints of two sides) is parallel to the third side and half its length. Here, \( VX \) is the midsegment, so \( TU = 2 \times VX \).

Step2: Substitute given expressions

Given \( TU = z + 39 \) and \( VX = 2z \), substitute into the equation: \( z + 39 = 2(2z) \).

Step3: Solve for \( z \)

Simplify the right side: \( z + 39 = 4z \).
Subtract \( z \) from both sides: \( 39 = 3z \).
Divide both sides by 3: \( z = \frac{39}{3} = 13 \).

Answer:

\( 13 \)