Question

QS is a mid-segment for triangle RUTIf TU= z + 2 and QS= z What is the value of z?

Answer 1

We can use the triangle mid-segment theorem to understand this problem better.

The midsegment of a triangle is parallel to the third side of the triangle and it’s always equal to 1/2 of the length of the third side.

From the image, we can say:

`QS=(1)/(2)TU`

Given the information for QS and TU, we can find the value of z:

`\begin{gathered} QS=(1)/(2)TU \\ z=(1)/(2)(z+2) \\ z=(1)/(2)z+(1)/(2)(2) \\ z=(1)/(2)z+1 \\ z-(1)/(2)z=1 \\ (1)/(2)z=1 \\ z=(1)/((1)/(2)) \\ z=2 \end{gathered}`

Thus, the value of z is

z = 2