Visualizing solid shapes!!!
- 1. VISUALIZING SOLID SHAPES!!! PRESENTED BY : SAACHI CHAUHAN
- 2. CONTENTS… • WHAT ARE SHAPES? • 2-DIMENSIONAL SHAPES • PROPERTIES OF 2-DIMENSIONAL SHAPES • 3-DIMENSIONAL SHAPES • PROPERTIES OF 3-DIMENSIONAL SHAPES • DIFFERENCE BETWEEN 2-DIMENSIONAL AND 3-DIMENSIONAL SHAPES • FACE’S • EDGE’S • VERTICES • POLYEDRONS , PRISM AND PYRAMIDS
- 3. WHAT ARE SHAPES? • A shape is a geometrical figure that can be described with mathematics. • For example, two-dimensional shapes like circles will fit inside of a flat plane. • Three-dimensional objects like cubes will not fit inside of a plane, because they are not flat.
- 4. 2-DIMENSIONAL SHAPES • These are two-dimensional shapes or flat plane geometry shapes. Their sides are made of straight or curved lines. They can have any number of sides. Plane figures made of lines are called polygons. Triangles and squares are examples of
- 5. PROPERTIES OF 2- DIMENSIONAL SHAPES • Two-dimensional shapes are planar. In the case of a coordinate system of more than two dimensions, then a 2-D shape would still depend on two coordinate directions. For example, in a spatial xyz coordinate system (which is three-dimensional) a two-dimensional shape would be expressed with points such as (x,y,0), (x,0,z), or (0,y,z). Therefore, it would depend on either x and y, x and z, or y and z. • 2-D shapes include the square, the triangle, the rhombus, etc. • To understand it more easily, you can say that 2-D shapes do not have prominent or rugged parts. For example, speaking two-dimensionally you would have a square, whereas three-dimensionally you would have a
- 6. 3-DIMENSIONAL SHAPES • A 3D shape is a solid which encloses a volume and has length, breadth and height.
- 7. 3-DIMENSIONAL SHAPES SOME MORE 3D SHAPES: CUBE AND SOME MORE…..
- 8. PROPERTIES OF 3- DIMENSIONAL SHAPES • Three-dimensional shapes have four properties that set them apart from two-dimensional shapes: faces, vertices, edges and volume. These properties not only allow you to determine whether the shape is two-or three-dimensional, but also which three-dimensional shape it is.
- 9. DIFFERENCE BETWEEN 2-D AND 3-D SHAPES 2-DIMENSIONAL • 2D is 'flat', using the X & Y (horizontal and vertical) axis', the image has only two dimensions and if turned to the side becomes a line. 3-DIMENSIONAL • 3D adds the ‘Z’ dimension. • This third dimension allows for rotation and depth. • It's essentially the difference between a painting and a sculpture.
- 10. Aq Platonic Solid Picture Number of Faces Shape of Faces Number of Faces at Each Vertex Number of Vertices Number of Edges Unfolded Polyhedron (Net) Tetrahedron 4 Equilateral Triangle (3-sided) 3 4 6 Cube 6 Square (4-sided) 3 8 12 Octahedron 8 Equilateral Triangle (3-sided) 4 6 12 Dodecahedron 12 Regular Pentagon (5-sided) 3 20 30 Icosahedron 20 Equilateral Triangle (3-sided) 5 12 30
- 11. Face • Part of a shape that is flat.(Or curved) • E.g. A cube has 6 of these.
- 12. Edge • The line where two faces meet. • E.g. A cube has 12 of these.
- 13. Vertex (Vertices) • The place where three or more edges meet. • This pyramid has 4 of these.
- 14. Polyhedrons In a convex polyhedron, the line segment joining any two points on the surface of the polyhedron lies entirely inside or on the polyhedron. A polyhedron some of whose plane sections are concave polygons is known as a concave polyhedron. Concave polygons have at least one interior angle greater than 180° and has some of its sides bent inward. Convex polyhedron
- 15. Prisms and pyramids A prism is a polyhedron with parallel congruent polygon bases and sides made of parallelograms. A pyramid is a polyhedron whose base is a polygon of any number of sides and whose lateral faces are triangles with a common vertex. Prisms and pyramids are named after the shape of their base. Maps represent the location of a place or object in relation to other places or objects. Prisms Pyramids
- 16. Prisms • Prisms have two identical, parallel faces joined to one another by rectangles. Examples are;
- 17. Pyramids • Pyramids have one face with at least 3 edges, the faces meeting these edges are ALL triangles. NOTE: Pyramids get their name from the shape of their base. • There are many more pyramids than these ones shown