Question

given the following, state yes or no as to whether the following pieces are represented. 1. yes bc = dc 2. yes $overrightarrow{ca}$ 3. yes $overrightarrow{gc}$ 4. yes $overrightarrow{db}$ 5. yes $angle{dgc}$ 6. no $angle{acb}+angle{bcf}=angle{acf}$ 7. no $cdot k$ 8. yes $angle{ecf}=angle{gcf}$

Explanation:

Step1: Analyze each statement

Check if the geometric - elements are present in the given figure.

Step2: For statement 1

Check if $BC = DC$. By observing the figure, we can see if the lengths are equal.

Step3: For statement 2

Check if ray $\overrightarrow{CA}$ is present. Locate the starting - point $C$ and the direction towards $A$.

Step4: For statement 3

Check if ray $\overrightarrow{GC}$ is present. Locate the starting - point $G$ and the direction towards $C$.

Step5: For statement 4

Check if line - segment $\overline{DB}$ is present. Locate points $D$ and $B$ and the line between them.

Step6: For statement 5

Check if $\angle DGC$ is present. Locate the three - point combination $D$, $G$, and $C$ forming an angle.

Step7: For statement 6

Check if $\angle ACB+\angle BCF=\angle ACF$. Analyze the angle - addition postulate in the figure.

Step8: For statement 7

Check if point $K$ is present. Look for the point labeled $K$ in the figure.

Step9: For statement 8

Check if $\angle ECF=\angle GCF$. Compare the two angles in the figure.

Answer:

1. yes
2. yes
3. yes
4. yes
5. yes
6. no
7. no
8. yes