"Translation of Graphics" PPT courseware

Description

"Translation of Graphics" PPT courseware

Observation and thinking------TV on the conveyor belt

Think about it:

1. In the picture above, have the shape and size of the TV on the conveyor belt changed before and after the movement?

2. If the TV screen moves forward 80cm, in what direction do other parts of the TV (such as the upper left corner of the TV) move? How far does it move?

Observation and thinking-----People on the escalator

1. Do the shapes and sizes of people on the escalator change before and after exercise?

2. If a person's feet move diagonally upward 10 meters, in what direction does the person's body move? How far did it move?

This change in the graph only changes the ______ of the graph but does not change the ______ of the graph.

Summary and summary

Concept: In a plane, move a figure along a certain direction

Moving a certain distance, this change in the graphics is called translation.

Points that can overlap before and after translation are called corresponding points

Translation only changes the ______ of the graph but does not change the ______ of the graph.

Give it a try:

1. Translation changes the graphics ( )

A. Shape B. Position

C. Size D. Shape, size and location

2. As shown in the figure, ∠DEF is obtained by translation of ∠ABC. ∠ABC=33°, then the degree of ∠DEF is _____.

3. RT△ABC is translated right along the straight line to BC to obtain △DEF. Which of the following conclusions is wrong ( )

A. △ABC ≌ △DEF

B. ∠DEF=90°

C. AC ∥DF and AC=DF

D. EC=CF

Example 1 As shown in the figure, in the quadrilateral ABCD, AD∥BC, AD�BC, AB=DC. Can you use the translation method to determine whether ∠B and ∠C are equal? Give your reasons.

Solution ∠B=∠C. The reason is as follows:

Translate the line segment AB to the right along AD to DE, so A and D, and B and E are two sets of corresponding points. According to the basic properties of translation, AD∥BE, AD=BE, because AD∥BC, because there is and is only one straight line parallel to AD through point B outside AD, and BE�BC, so point E is on side BC.

In the quadrilateral ABED, AD∥BE, AD=BE, so the quadrilateral ABED is a parallelogram, so AB=DE. Because AB=DC, so DE=DC, so ∠DEC=∠C. From ∠B=∠DEC, we can know ∠B=∠C.

summary

1. Definition of translation

In a plane, when a figure is moved a certain distance in a certain direction, this change in the figure translates.

2. Two elements of translation:

Translation direction and translation distance

3. Properties of translation:

1. After the graph is translated, the lines connecting corresponding points are parallel (or on the same straight line) and equal.

2. The shape obtained after translation is congruent with the shape before translation.

After the graphic is translated, the size and shape of the graphic remain unchanged.

Practice in class

1. Fill in the blanks

(1) Translate line segment AB 3cm to the right to get line segment CD. If AB=5 cm, then CD=____cm.

(2) Translate ∠ABC upward 10cm to get ∠EFG. If ∠ABC=52°, then ∠EFG=_____°, BF=_____cm.

(3) Translate the isosceles right angle △ ABC with an area of ​​30cm2 downward by 20cm to obtain △MNP. Then △MNP is a _____ triangle with an area of ​​_____cm2.

2. Choose

(1) Translation changes the graphics ( )

A position B size

C shape D position, size and shape

(2) After translation, each point on the graph has moved a certain distance in the same direction. The following statement is correct ( )

A Different points move different distances

B may be the same or different

C Different points move the same distance

D Unable to determine

As shown in the figure, the rectangle has a horizontal side length of a and a vertical side length of b. Translate the line segment A1A2 to the right by one unit to obtain B1B2, and obtain the closed figure A1A2 B2B1 (that is, the shaded part). Find the remainder after removing the shaded part. Part area?

As shown in the figure, the rectangle has a horizontal side length of a and a vertical side length of b. Translate the polyline A1A2A3 to the right by one unit to obtain B1B2B3, and obtain the closed figure A1A2A3B3B2B1 (that is, the shaded part). Find the remaining part after removing the shaded part. area?

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Update Time: 2024-07-10

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 2 industry PPT template

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