What are the two regular polygons that can cover the ground??? 30

Only triangles can. Anything else is absolutely impossible.

is a regular triangle or square.

All two types of stool polygons can be covered with floors with:

1. Regular triangle.

with regular octagons;

2. Regular triangle letter height and positive hexagonal return to Tan travel shape.

3. Regular triangle and regular dodecagonal;

4. Square and octagon;

5. Triangles and squares.

The sum of the inner angles of the polygon and the inner angles of the n-sided of the theorem is equal to: (n 2) 180°, then the number of each inner angle of the regular polygon is: (n 2) 180° n.

Polygons with equal sides and equal corners are called regular polygons (polygons: the number of sides is greater than or equal to 3). The center of the circumscribed circle of a regular polygon is called the center of the regular polygon.

The length of the line connecting the center to the vertices of a regular polygon is called the radius, and the distance between the center and the edge is called the edge centr. Quiet friends.

The axis of symmetry of a regular polygon - odd edges: the midpoint of connecting a vertex and the edge opposite the vertex is the axis of symmetry; Even-numbered edges: Connecting the midpoint of two opposite edges, or connecting two vertices that are symmetrical, are axes of symmetry. The number of sides of a regular n-sided is n, and the number of axes of symmetry is n.

Mosaic rules. In regular polygons, there are only three types that can be used to fill a plane without gaps in between: regular triangles, squares, and regular hexagons. Because each angle of a regular triangle is equal to 60 degrees, when the six regular triangles are put together, the sum of the angles of the hexagram at the common vertex is equal to 360 degrees.

Each corner of the square is equal to 90 degrees, so when the four squares are put together, the sum of the four corners at the common vertex is exactly equal to 360 degrees; Each corner of a regular hexagon is equal to 120 degrees, and when three regular hexagons are put together, the sum of the three angles at the common vertex is also equal to 360 degrees, which cannot be met if other regular polygons are used.

For example, each corner of a regular pentagon is equal to 108 degrees, and if you put three regular pentagons together, the sum of the three angles at the common vertex is 108 degrees*3=324 degrees, and there is a gap less than 360 degrees. And the fourth regular pentagon cannot be placed in the gap, because 108 degrees * 4 = 432 degrees, which is greater than 360 degrees.

Each inner angle of a regular triangle is 60°, divisible by 360°, and densely paved;

Each inner angle of the regular quadrilateral is 90°, and 4 can be densely paved;

Each inner angle of a regular hexagon is 120 °, which is divisible by 360 °, and can be densely spread with ridges, so the answer is: a regular triangle, a regular four-sided sock blind shape, and a regular hexagon

a, the number of an internal angle of the three sleepy angles is 180-360 3 = 60 °, which is the approximate number of 360 °, which can be inlaid with the plane and does not conform to the theme;

b. The number of an internal angle of the regular quadrilateral is 180-360 4=90 °, which is the approximate number of 360 °, which can be inlaid with the plane, which does not conform to the theme of the Ant Nian;

c. The number of an internal angle of a regular pentagon is 180-360 5=108°, which is not a divisor of 360°, and cannot be mosaic, which is in line with the theme;

d. The number of an internal angle of a regular hexagon is 180-360 6=120°, which is the approximate number of 360°, which can be mosaic and does not conform to the theme

Therefore, C

Being able to cover the ground means that its sum value is 360°. Positive n deformation, the sum of its internal angles is 180°(n-2), so each internal angle is 180°(n-2) n. Able to cover the ground, therefore requires 360° Each interior angle = integer, ie.

m=360° [180°(n-2) n]=2n (n-2)=[2(n-2)+4] (n-2)=2+4 (n-2) is an integer, therefore.

When n=3, m=6;n=4,m=4;n=6, m=3 meet the requirements.

In fact, 4 (n-2) is an integer, requiring 4>=n-2 and n<=6. So all of the above is met by all the requirements. i.e. triangles, squares and regular hexagons.

The condition for paving the ground with a regular multi-segment regular square is that the whole common multiple of the inner angle is 360°, that is, it can be paved with a face.

The same kind of regular polygon can be used to cover the ground with regular triangles, squares, and regular hexagons.

The reason why you can spread the ground with a regular hexagon is that the number of internal angles of a hexagon is 120°, which is the common divisor of 360°.

The reason why you can't cover the ground with a pentagon is that the inner angle of the pentagon is 108°, which is not a 360° approximate number of gongxiao beams, and it can't be covered with one face.

According to the conditions of plane figure mosaic: to judge whether a figure can be mosaic, just look at whether several corners at the same vertex can form a perimeter angle. If it can be composed of cherry blossom rows, it means that it can be inlaid in a plane; Otherwise, you can't, and you can get the answer.

Xie Lizhong: With a kind of regular polygon inlay, only three regular polygons, such as square, regular hexagon, and equilateral triangle, can be inlaid into a plane pattern.

What cannot be covered with ground is a regular decagonal;

Therefore, it is chosen. This question examines the plane mosaic, and the knowledge point used is that only one regular polygon can be used to cover the ground is a regular triangle or regular quadrilateral or regular hexagon.

The polygon group that can cover the ground has a characteristic of Bird's Spring, that is, the inner corner can form a circumferential angle.

Because an n-sided shape can be divided into (n-2) triangles. So the sum of the internal angles of the n-sided shape: (n-2) 180

Therefore: the number of edges and the number of angles inside.

Therefore, the answer should be b, c