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Authoritative PPT Summary
"Similar Polygons" similar PPT courseware for graphics
Knowledge points
The shape of two figures is ________, but the size and position of the figures are __________. Such figures are called similar figures.
relationship between similar figures
Two figures are similar, and one figure can be seen as enlarging or reducing the other figure.
Properties of similar polygons
The ratios of the corresponding heights, the ratios of the corresponding angle bisectors, the ratios of the corresponding midlines, and the ratios of the corresponding perimeters of similar polygons are all equal to the similarity ratio.
The ratio of diagonals to similar polygons is equal to the similarity ratio.
Similar polygons correspond to similar triangles, and the similarity ratio is equal to the similarity ratio of similar polygons.
The ratio of the areas of similar polygons is equal to the square of the similarity ratio.
The ratio of the areas of similar polygons to corresponding triangles is equal to the square of the similarity ratio of similar polygons.
Determine whether two polygons are similar
Solution: ∵ The four sides of a square and a rhombus are equal.
∴ Their corresponding sides are proportional, k = 3 : 4.
∵ The four interior angles of a square are all right angles, while the interior angles of a rhombus are obtuse and acute.
∴ Their corresponding angles are not equal.
∴ This set of graphics is not similar.
Practice in class
1. Judgment:
(1) Any two rectangles are similar figures ( )
(2) Any two circles are similar figures ( )
(3) Two quadrilaterals with equal corresponding angles are similar polygons ( )
(4) Two regular pentagons are similar polygons ( )
(5) Two congruent triangles are similar polygons ( )
(6) Two rhombuses are similar polygons ( )
(7) Two similar polygons, corresponding sides are proportional ( )
2. Pentagon ABCDE is similar to pentagon A′B′C′D′E′, and their similarity ratio is 1:3.
(1) If ∠D=135°, then ∠D′= ______.
(2) If A′B′=15cm, then AB= ______.
3. The side lengths of a polygon are 2, 3, 4, 5, and 6 respectively, and the shortest side length of another polygon similar to it is 6, then the longest side of this polygon is ______.
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For more information about the "Similarity of Similar Polygonal Figures" PPT courseware, please click the Similarity ppt tag of similar polygonal ppt figures.
"Positional similarity of similar polygons and figures" PPT courseware 2:
"Positional Similarity of Similar Polygons and Figures" PPT Courseware 2 1. If two ________ polygons ____________________ intersect at one point, we call the two figures similar figures. The intersection point is called ________, and the similarity ratio at this time is also called __..
"Positional Similarity of Similar Polygons and Figures" PPT courseware:
"Positional Similarity of Similar Polygons and Figures" PPT courseware 1. Two polygons with corresponding angles ________ and corresponding sides ________ are called ________. 2. The ratio of the perimeters of two similar polygons is equal to their __________; the ratio of the areas of similar polygons is equal to their _..
"Similar Polygons" PPT courseware:
"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'..