Question

CD is the midsegment of trapezoid WXYZ. you must show your work to all the parts below

Answer 1

Given that CD is the midsegment of the trapezoid WXYZ

From the properties of Midsegment of trapezoid we have :

0. The midsegment of a trapezoid is parallel to each base.

,

1. The length of the midsegment of a trapezoid is equal to half the sum of the lengths of its bases.

`\text{length of mid segment =}(a+b)/(2)`

In the given figur, the mid segement CD= 22

length of parallel side is WZ=x+3

and the length of another side XY = 4x+1

so apply the mid segment length formula :

`\begin{gathered} CD=(WZ+XY)/(2) \\ 22=(x+3+4x+1)/(2) \\ 5x+4=44 \\ 5x=40 \\ x=8 \end{gathered}`

x=8,

For, XY :

Substitute x=8 into the given length expression of XY

XY =4x+1

XY=4(8)+1

XY=33

For, WZ :

Substitute x=8 into the given expression length of WZ

WZ=x+3

WZ=8+3

WZ=11

Answer :

a). x = 8

b). XY = 33

c). WZ = 11