Question

when you are communicating with others, it is important that you include sufficient information in the diagram. use the diagram below to determine which of the following statements you can assume to be true. explain your reasoning.
i. points d, g, and i are collinear. no
ii. points a, c, and b are collinear. yes
iii. (overrightarrow{eg}) and (overrightarrow{ah}) are perpendicular. yes
iv. (overrightarrow{af}) and (overrightarrow{bd}) are perpendicular.
v. (overrightarrow{af}) and (overrightarrow{bd}) are coplanar.
vi. (overrightarrow{eg}) and (overrightarrow{bd}) do not intersect. yes
vii. (overrightarrow{af}) and (overrightarrow{bd}) intersect. yes
viii. (overrightarrow{ac}) and (overrightarrow{fh}) are the same line. yes
use the diagram in part (b) to write two statements you can assume to be true and two statements you cannot assume to be true. your statements should be different from those given in part (b). explain your reasoning.

Explanation:

Step1: Recall collinear - points definition

Points are collinear if they lie on the same line.

Step2: Recall perpendicular - lines definition

Lines are perpendicular if they intersect at a right - angle.

Step3: Recall coplanar - lines definition

Lines are coplanar if they lie in the same plane.

Step4: Analyze statements

• For points D, G, I: They do not lie on the same line, so they are not collinear.
• For points A, C, B: They lie on the same line, so they are collinear.
• For $\overrightarrow{EG}$ and $\overrightarrow{AH}$: They intersect at a right - angle, so they are perpendicular.
• For $\overrightarrow{AF}$ and $\overrightarrow{BD}$: They do not intersect at a right - angle, so they are not perpendicular.
• For $\overrightarrow{AF}$ and $\overrightarrow{BD}$: They lie in the same plane, so they are coplanar.
• For $\overrightarrow{EG}$ and $\overrightarrow{BD}$: From the diagram, they do not intersect.
• For $\overrightarrow{AF}$ and $\overrightarrow{BD}$: They intersect at a point.
• For $\overrightarrow{AC}$ and $\overrightarrow{FH}$: They are the same line.

Answer:

i. No, points D, G, and I are not collinear as they do not lie on the same line.
ii. Yes, points A, C, and B are collinear as they lie on the same line.
iii. Yes, $\overrightarrow{EG}$ and $\overrightarrow{AH}$ are perpendicular as they intersect at a right - angle.
iv. No, $\overrightarrow{AF}$ and $\overrightarrow{BD}$ are not perpendicular as they do not intersect at a right - angle.
v. Yes, $\overrightarrow{AF}$ and $\overrightarrow{BD}$ are coplanar as they lie in the same plane.
vi. Yes, $\overrightarrow{EG}$ and $\overrightarrow{BD}$ do not intersect as shown in the diagram.
vii. Yes, $\overrightarrow{AF}$ and $\overrightarrow{BD}$ intersect as seen in the diagram.
viii. Yes, $\overrightarrow{AC}$ and $\overrightarrow{FH}$ are the same line as indicated in the diagram.