Question

$\overleftrightarrow{\text{AE}},\overleftrightarrow{\text{BF}},\overleftrightarrow{\text{CG}}$and $\overleftrightarrow{\text{DH}}$ are parallel, with $\text{EF}=\text{FG}=\text{GH}$. Complete.

If $\text{AC}=\mathbf{12}$, then$\text{CD}=$ ? .

Short answer

The length of CD is 6 units.

Step-by-step solution

Step 1. Consider the diagram.

The parallel lines are shown as:

AE, BF, CG and DH are parallel to each other and $EF=FG=GH$.

The length of AC is 12 units

Step 2. Show the calculation.

Here, ADHE is the trapezoid as AE is parallel to DH.

As $EF=FG=GH$ and AE, BF, CG and DH are parallel to each other then the lines BF and CG are the midsegment of the trapezoid.

Hence,

$AB=BC=CD$

The length of CD is calculated as:

$\begin{array}{c}AC=AB+BC\\ 12=CD+CD\\ 12=2CD\\ CD=6\end{array}$

Thus, the length of CD is 6 units.

Step 3. State the conclusion.

Therefore, the length of CD is 6 units.