"From Three Views to Geometry" Projection and View PPT

"From Three Views to Geometry" Projection and View PPT

Part One Content: Lesson Introduction

Question: Please carefully observe the following regular hexagonal prism and draw its three views. Tell the correspondence between the line segments in the main view you drew and the middle edge of the regular hexagonal prism, and the virtual and real conditions of the line segments in the view.

From three views to geometry PPT, the second part: gaining new knowledge

Knowledge point: Determine geometry from three views

One view cannot determine the spatial shape of an object. When describing geometry or physical prototypes based on three views, the views must be compared. Imagine the front and rear, upper and lower sides, and left and right sides of the three-dimensional figure based on the front view, top view, and left view, and then Then take it all together and consider the overall graphics.

Imagine the geometry from three views:

(1) Method: When imagining a three-dimensional figure from three views, first imagine the front, top and left side of the three-dimensional figure based on the front view, top view, and left view respectively, and then consider the overall figure together.

(2) Process: Imagine the geometric shape from three views, which can be analyzed through the following methods.

Example 1 As shown in the figure, name the three-dimensional figures according to the three views (1) and (2) respectively.

Analysis: When imagining a three-dimensional figure from three views, first imagine the front, top and left sides of the three-dimensional figure based on the main view, top view and left view respectively, and then consider the overall figure together.

Solution: (1) When looking at the three-dimensional figure from three directions, the views are all rectangular. We can imagine that the three-dimensional figure is a cuboid, as shown in Figure (1).

(2) When looking at a three-dimensional figure from the front or side, the view is an isosceles triangle; when viewed from above, you can imagine that the three-dimensional figure is a cone, as shown in Figure (2).

Summarize

Imagine the shape of the object based on the three views of the object. Generally, the shape of the object on the plane is determined from the top view, and its shape in space is imagined based on the left view and front view to determine the shape of the object.

Example 2 Describe the shape of the object based on the three views of the object (as shown in the figure).

Analysis: From the main view, we can see that the front of the object is a regular pentagon; from the top view, we can see that the object has two faces when viewed from top to bottom, which is a rectangle, and their intersection is an edge (represented by the solid line in the middle). It can be seen that , there are two other edges (represented by the dotted lines) that are blocked; as can be seen from the left view, the view of the two faces on the left side of the object is a rectangle, and their intersection is an edge (represented by the solid line in the middle), which can be seen. Comprehensive It can be seen from each view that the shape of the object is a regular pentagonal prism.

Knowledge point: Determine the number of geometric entities from three views

Example 3 A geometric body is made up of small cubes of the same size. The shape of the geometry seen from above is as shown in the figure. The number in the small square represents the number of small cubes at that position. When seen from the front The shape of the geometry is () in the picture

Guidance: In the top view, the first column has the highest 3 small cubes, the second column has the highest 2 small cubes, and the third column has the highest 3 small cubes. Therefore, the main view can be seen from left to right. The number of small cubes is 3, 2, and 3, so choose D.

From three views to geometry PPT, the third part: class summary

Knowledge summary

1. What did you gain from studying this class?

2. When imagining the shape of a three-dimensional figure from the three views of a three-dimensional figure, do you have any good ideas? Communicate with your peers.

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For more information about the PPT courseware "Projection and View from Three Views to Geometry", please click the Projection and View PPT From Three Views to Geometry PPT tab.