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"Translation" Intersecting Lines and Parallel Lines PPT Courseware
Discussion and exchange
How to draw a row of snowmen with the same shape and size as Figure 5.4-2 on page 30 of the book on a piece of paper
Think twice and discuss it in groups first! Start painting and you will be a great painter in the future!
Is the snowman in your painting the same as the one in the book? How do you draw it?
Observe and think
1. Did the shape, size, and position of the snowman change before and after the exercise?
2. When snowman A moves to the position of snowman B, how does snowman A’s nose tip A move? Where has it moved? What about hat top B?
3. Connect several groups of corresponding points (such as: A and A', B and B', C and C') and observe the line segments. What is the relationship between their positions and lengths?
4. When you draw line segments connecting other corresponding points, do they still have the same relationship as before?
definition
In a plane, moving a figure a certain distance in a certain direction is called translation.
1. After translation, each point on the graph has moved a _________ distance along ____________, so
(1) After translation, the corresponding line segment _________
(2) After translation, the corresponding angle ___________
(3) After translation, the line segments connected to the corresponding points ____________
(4) After translation, the new shape and the original shape are a pair of _________
2. Nature of translation
After translation, the line segments connected to the corresponding points are parallel and equal, the corresponding line segments are parallel and equal, and the corresponding angles are equal.
How to translate a triangle
Example After translation, the vertex A of triangle ABC moves to point D. Draw the translated triangle.
Analysis: Suppose vertices B and C are translated to E and F respectively,
According to "after translation, the line segments connected to the corresponding points are parallel and equal", it can be seen that the line segments BE, CF and AD are parallel and equal.
Solution: As shown in the figure, draw line segments BE and CF through points B and C respectively so that they are parallel and equal to line segment AD, connecting DE, DF and EF. Triangle DEF is the translated shape of triangle ABC.
Discuss
Among the following phenomena, the ones that belong to translation are:
(1) Movement of the needle tube during injection
(2) The bullet fired
(3) The train runs on straight rails
(4) When cold water is heated, small bubbles rise and turn into large bubbles
(5) People walking on the stairs
(6) The swing of the pendulum
(7) The aircraft slides on the straight runway before takeoff
Thoughts and Questions
1. Does the classroom door move horizontally when it is opened or closed?
2. Is the athlete's running a translation?
3. Is the lift of the elevator in the building a translational movement?
4. Does a child’s skateboard move horizontally?
5. Are skiers sliding in translation?
6. Is swinging a translation?
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