Mathematics courseware of the second volume of the ninth grade: similarity
learning target
1. Understand the potential forms through experiments, operations and thinking activities.
2. Will use the potential principle to enlarge or reduce a graph.
4. Understand the role of mathematics in real life and enhance confidence in learning mathematics well.
Key point: Understand that location similarity is determined by location similarity center and similarity ratio.
Difficulty: making similar figures and finding the similarity ratio of similar figures.
Preview:
1. Textbook 1 10 Page Math Lab.
2. Practice and thinking of the textbook 1 10.
Second, inquiry learning:
1. As shown in the figure, the quadrilateral ABCD is known, and it is enlarged with a ruler, so that the ratio of the corresponding line segments before and after enlargement is 1: 2.
2. As shown in the figure, O is known as the origin of coordinates, and the coordinates of B and C are (3,-1) and (2, 1) respectively.
(1) Zoom △OBC to the left side of the Y axis with O as the similarity center (that is, the similarity ratio between the new image and the original image is 2), and draw a graph;
(2) Write the coordinates of points B' and C' corresponding to points B and C respectively;
(3) If the coordinate of a point M in △OBC is (x, y), write the coordinate of the corresponding point M'.
3. Build paths around the flower beds of rectangular ABCD with AB=30m and AD=20m.
(1) If the widths of the surrounding paths are equal, as shown in the figure (1), is the rectangle A' b' c' d' surrounded by a path similar to the rectangle ABCD? Please explain the reason.
(2) If the widths of two opposite paths are equal, as shown in Figure (2), what is the ratio of the widths x and y of the paths, so that the rectangle A ′ b ′ c ′ d ′ enclosed by the paths is similar to the rectangle ABCD? Please explain the reason.
Three class assignments:
1. As a method of quasi-graph, the graph can be enlarged or reduced, and the quasi-center position can be selected in A. Outside the original graph B. Inside the original graph C. On the edge of the original graph D. Anywhere.
2. If two graphs are similar, they must be similar. On the contrary, if two graphs are similar, they
A. It must be similar to B. It must not be similar to C. It must not intersect with the connecting line of similar points of D.
3. As shown in the figure, the vertex coordinates of right-angle OABC are O (0 0,0), A (6 6,0), B (6 6,4) and C (0 0,4) respectively. Draw the potential diagram OA' b' c of right-angle OABC with point O as the potential center, so that its area is equal to that of right-angle OABC, and write a' and a' respectively.
4. Print a rectangular billboard, as shown in the figure, with a printing area of 32dm2, upper and lower blanks of 65,438+0dm, and margins of 0.5dm on both sides. Let the length of the printed part be xdm from top to bottom. The area around the blank area is Sdm2.
(1) Find the relationship between S and X;
(2) What is the length and width of the paper for printing this billboard when the surrounding blank area is required to be 18dm2?
(3) Under the condition of (2), are the inner and outer rectangles similar? Explain why.
The ninth grade second volume mathematics courseware: the rotation of graphics
Teaching objectives
1, through concrete examples to understand the rotation transformation of graphics; Cultivate hands-on ability and rational reasoning ability as well as the habit and ability of mathematical reasoning.
2. Through the rotation of various graphics, the main factors to experience the rotation of graphics are the rotation center and rotation angle.
teaching process
First, create a situation
In daily life, besides the parallel motion of objects, we can also see the rotation of many objects: the motion of planets in the universe, the motion of particles in the microscopic world, and the motion in life.
In the picture below, all the graphics can be regarded as wonderful pictures produced by the rotation of one or several basic plane graphics.
What are the characteristics of these figures?
These figures can be regarded as new figures formed by a figure rotating around a certain point.
As shown in the figure, the rotation of the ball on a simple pendulum changes from position p to position P'. Movement like this is called rotation, and this suspension point is called the center of rotation of the ball.
The concept of rotation:
Note: When the graph rotates, each point rotates by the same angle in the same way, but each point takes a different route.
Exercise: 1 Among the following phenomena, () belongs to rotation.
(1) The groundwater level is decreasing year by year; ② the movement of conveyor belt; ③ the rotation of the steering wheel; (4) the rotation of the faucet switch; (5) the movement of the pendulum; 6. Swing. A.2 B.3 C.4 D.5
2. The bauhinia pattern in the center of the regional flag of the Hong Kong Special Administrative Region consists of five identical petals. How many times did one of them rotate?
Second, explore and summarize.
As shown in figure (1), point A rotates 80 around point O to the position of point A', then points A' and A are called corresponding points, point O is the rotation center, and ∠AOA' is equal to the rotation angle of 80.
As shown in Figure (2), line segment AB turns 60 degrees around point O to the position of line segment A'B', then line segment A'B' and line segment AB are called corresponding line segments, and point B' and point B' are corresponding points.
As shown in Figure (3), when △AOB rotates around point O by 45 to △ a ′ ob ′, the rotation center in the figure is one point, the rotation angle is, the corresponding point is, the corresponding line segment is, ∠A and ∠ a ′ are called corresponding angles, and there are also corresponding angles in the figure.
It is concluded that in the process of rotation, the center of rotation is determined by, and.
Third, business exploration activities.
1. Rotate △ABC clockwise around point O to the position of △ A ′ B ′ C ′, and measure the degrees of ∠ AOA ′, ∠ Bob ′ and ∠ COC ′, and the lengths of line segments AO and ao ′, bo and bo ′, co and co ′.
What did you find? △ABC and△ A ′ B ′ C ′ are congruent triangles?
Thinking: What is the relationship between the rotation of the figure and the central symmetry of the figure?
Fourth, practical application.
Example 1 Given point A and point O, point A rotates 30 around point O and then draws point A'.
1. Given the line segment AB and the point O, draw a picture after the line segment AB rotates 80 counterclockwise around the point O. ..
2. Given △ ABC and point O, draw a picture after △ ABC rotates 80 counterclockwise around point O. ..
3. What if it is changed to a polygon? Can you summarize the method of rotation drawing?
Complete textbook P58 "Example 1, Example 2"
Example 2 Think about the textbook P60 "Communication and Discovery" and complete "Example 4"
Exercise: As shown in the figure, △ABC is an equilateral triangle, D is a point on the side of BC, and △ABD rotates to reach the position of △ACE.
(1) What is the center of rotation? (2) How many degrees has it rotated?
(3) If m is the midpoint of AB, where does point M turn after the above rotation?
Verb (abbreviation of verb) consolidates and improves.
1, textbook P74 exercise 1, 2, 3
2. As shown in the figure, △ABD rotates clockwise into △ACE, and write down the corresponding vertex, corresponding angle, corresponding line segment, rotation center and rotation angle in the figure, and try to write equal line segments and angles (referring to the sides and angles in two triangles) in the figure.
3. In the rectangular ABCD, connect BD, rotate △ABD to △CDB, and write the rotation center and rotation angle.
Sixth, the class summary
By teachers and students * * * summed up the relevant points of graphic rotation:
(1) The rotation of a graph is to rotate a graph clockwise (counterclockwise) around a point for a certain angle;
(2) The center of rotation remains stationary during the rotation;
(3) The rotation of the graph is determined by the rotation center and rotation angle.
Seven. distribute
Textbook P78 Exercise 15.2 No.65438+0,4.