2-D and 3-D shapes

PREPARED BY: DYATLOVA IRINA, LINEVICH IRINA, POLINA PALIY, OLGA KONDRATYEVA, DRAGANOV ALEXANDER, ARINA BUSHOVA, IGOR SOLOGUB, KRISTINA KUZMENKO, KUZMENKOVA DARYA, STYAZHKIN VALERIY, RUDNEVA ZHANNA, KOLODINA ANASTASYA

Polygon - a closed line, which is formed by taking an any points A1, A2, ..., An and connect them in series segments.

arbitrary polygon

And now the question: which of these falls from a number of polygons?

Look closely at the second polygon - it is essentially different from all others. With what? It is not convex. This is certainly a mathematical name, but with the human intuition is not at odds.

Well, as we consider only convex polygons

In any polygon is the sum of the interior angles of 180 o (n-2) 180o(n-2), where the letter «nn» denotes the number of corners of the polygon

Triangles - Theory

Equilateral triangles

Isosceles triangles

2 equal sides2 equal angles1 line of symmetry3 equal sides

3 equal angles3 line of symmetry

Right-angled triangle

Scalene triangle

1 angle is a right angleSome right-angled triangles are isoscelesSome right-angled triangles are scalene

No equal sidesNo equal anglesNo lines of symmetry

Exercises№1 Write the name of each triangle. Some triangles may have more than one name.

a) Isosceles;

b)Isosceles, equilateral;

c)Right-angled, isosceles;

d)Scalene; e)Isosceles;

f)Equilateral, isosceles

№2 Copy the Venn diagram. Look again at the triangles in exercise 1. Complete the diagram and write the letter for each triangle in the correct section.

a

be

fc

d

QuadrilateralsTypes of quadrilaterals

1. А Square (4 equal sides, 4 equal angles, 4 lines of symmetry)

2. A Rectangle (2 pairs of equal sides, 4 right angles, 2 lines of symmetry)

3. A Rhombus (4 equal sides, opposite angles equal, opposite lines parallel, no lines of symmetry)

4. A Parallelogram (opposite sides are equal and parallel, no lines of symmetry)

5. A Kite (2 pairs of adjacent sides are equal, 1 line of symmetry)

6. A Trapezium ( a pair of parallel sides, 0 or 1 line of symmetry)

1. Name each of these quadrilaterals

«Symmetrical shapes and patterns»Rule Some shapes and patterns are symmetrical. They have

lines of symmetry, or reflective symmetry. Look at this kite.

Imagine it folded the middle. The two sides would look exactly the same. That fold line is the line of symmetry and shows whether a shape or pattern is symmetrical.

Exercises1)Write how many lines of symmetry there are on each of these shapes.

a) b) c)

d) e) f)

Prisms and PyramidsPRISM IT’S A GEOMETRIC SHAPE, A POLYHEDRON WITH TWO EQUAL AND PARALLEL FACES, CALLED BASES AND HAVING THE SHAPE OF A POLYGON.

PYRAMID IS A MULTI — FACETED GEOMETRIC SHAPE BASED ON A POLYGON AND THE VERGE ARE BASED TRIANGLES WITH A COMMON VERTEX.

WRITE THE NAME FOR EACH SHAPE.

Thank you for your attention!