Question

This image shows a geometric diagram with the following elements: Points D, G, H, I, F, and m: These points are labeled on the diagram. Collinear Points G, H, and I: These points lie on a straight line that extends from point m to point I. Parallelogram: The points D, G, H, and I form a parallelogram, a four-sided figure with opposite sides parallel and equal in length. Point F: This point is located inside the parallelogram but is not on the collinear line. Point m: Point m appears to be outside the parallelogram and is connected to point I by the collinear line G, H, and I. This diagram seems to illustrate a geometry problem involving the properties of parallelograms, collinear points, or vector analysis.
Given the image, identify the following statements as either True or False.(7 points)
True False

This plane can be named plane D.
m is a point on the plane.
H is a point on the plane.
D is a point on the plane.
The image shows IF¯¯¯¯¯¯.
The line shown in the image can only be named 1 way.
H is the midpoint of GI¯¯¯¯¯¯¯.

Answer 1

To evaluate the statements based on the provided description of the geometric diagram, here's the analysis:

1. **This plane can be named plane D.**
**False** - A plane cannot be named by a single point. A plane is typically named by three non-collinear points or a specific designation (e.g., Plane ABC).

2. **m is a point on the plane.**
**False** - The description states that point m is outside the parallelogram and is not indicated as being on the plane formed by points D, G, H, and I.

3. **H is a point on the plane.**
**True** - Since H is one of the vertices of the parallelogram (which consists of points D, G, H, and I), it lies on the defined plane.

4. **D is a point on the plane.**
**True** - Similarly, point D is another vertex of the parallelogram, therefore, it is also on the plane.

5. **The image shows IF¯¯¯¯¯¯.**
**False** - Since F is a point inside the parallelogram and I is a point on the line defined by G, H, and I, there is no indication of a line segment IF shown in the diagram from the provided description.

6. **The line shown in the image can only be named 1 way.**
**False** - Lines can be named in multiple ways depending on the points used for naming. For instance, the line could potentially be named as line GI, line HI, or line GH.

7. **H is the midpoint of GI¯¯¯¯¯¯¯.**
**False** - Without additional information confirming that H bisects the segment GI, we cannot assume H is the midpoint.

So the summarized truth values for the statements are:

1. False
2. False
3. True
4. True
5. False
6. False
7. False