"Similar Polygons" PPT courseware

Description

"Similar Polygons" PPT courseware

∠A=150° AB=6.5mm ∠A'=150° A'B'=13mm

∠B=120° BC=5.5mm ∠B'=150° B'C'=11mm

∠C=105° CD=6mm ∠C'=105° C'D'=12mm

∠D=135° DE=5mm ∠D'=135° D'E'=10mm

∠E=120° EF=7.5mm ∠E'=120° E'F'=15mm

∠F=90° FG=4.5mm ∠F'=90° F'G'=9mm

What conclusions can you draw from the above data?

in conclusion:

Hexagon ABCDEF and hexagon A1B1C1D1E1F1 are figures with the same shape;

Their six angles are all equal and are called corresponding angles; the ratios of their six sides are all equal and they are called corresponding sides.

Can you try to define similar polygons?

Read the first two paragraphs on pages P120-121 of the textbook, and then answer the following questions (time 3 minutes):

①How many conditions must be met for polygons to be similar?

②What are the requirements for notation of similar polygons?

③What is similarity ratio? What should we pay attention to when looking for similar ratios?

gain new knowledge

Two polygons whose angles are equal and whose sides are proportional are called similar polygons.

It is written as: hexagon ABCDEF ∽ hexagon A1B1C1D1E1F1

Note: When remembering that two polygons are similar, write the letters of the corresponding vertices in the corresponding positions.

The ratio of corresponding sides of similar polygons is called the similarity ratio

The similarity ratio is related to the order of the narrative.

Take a look and discuss it

1. Observe the two sets of graphics below. Are the two graphics in Figure 4-12 (1) similar? Why? Figure 4-12

What about the two figures in (2)? Communicate with your deskmates.

2. If two polygons are not similar, is it possible that their angles are equal? Is it possible that their sides are proportional to each other?

Try it: Are each of the following sets of shapes similar polygons? Try to explain why.

(1) Equilateral triangle ABC and equilateral triangle DEF;

(2) Square ABCD and square EFGH.

Solution: (1) Equilateral triangle ABC is similar to equilateral triangle DEF

Since each angle of an equilateral triangle is equal to 60°, ∠A=∠D= 60°, ∠B=∠E= 60°, ∠C=∠F= 60°;

Since all three sides of an equilateral triangle are equal, so

AB/DE=BC/EF=CA/FD

Therefore, equilateral triangle ABC is similar to equilateral triangle DEF;

Solution: (2) Square ABCD is similar to square EFGH.

Since each angle of a square is a right angle, ∠A=∠E= 90°, ∠B=∠F= 90°, ∠C=∠G= 90°, ∠D=∠H= 90°;

Since the four sides of a square are equal, so

AB/EF=BC/FG=CD/GH=DA/HE

So square ABCD is similar to square EFGH

summary

Two polygons whose corresponding angles are equal and whose corresponding sides are proportional are called similar polygons

The ratio of corresponding sides of similar polygons is called the similarity ratio

The similarity ratio is related to the order of the narrative.

Corresponding angles of similar polygons are equal and corresponding sides are proportional.

If two polygons are dissimilar, then their angles may be equal and their sides may be proportional.

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Update Time: 2024-11-12

This template belongs to Mathematics courseware Qingdao Edition Ninth Grade Mathematics Volume 1 industry PPT template

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