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Problem solving and geometry Presentation prepared by Lera Antonova-Rudzevich Gerbrant Agnes Stroganova Aleksandra Dyatlov Dmitry Dmitry Ovcharov Alexander Shevchenko Dmitry Peretokin Knyazeva Alisa Dedova Darya Gozh Marya Coordinates Students 7B class Alexander Shevchenko Dmitry Peretokin Coordinates Coordinates are used to show an exact position of a point on a grid. Two numbers from the xaxis and y-axis show the position The coordinates of A are (2,3). Coordinates are always written in brackets and the numbers are separated by a comma. practice Find it in the city Cinema (1;7) Hospital (0;0) Shop (2;3) Street (-7;-6) House (-9;1) School (-5;7) Movement geometry Students 7B class Gerbrant Agnes, Stroganova Aleksandra Movement geometry Translation Rotation A shape can be rotated about a point, clockwise or anti-clockwise Reflection This is sometimes called flipping over. Shape A is reflected. The dotted line is a line of reflection. This is sliding a shape across, up, down or diagonally, without rotating or flipping over. Shape A has moved across and down. Exercise 1. Look at this grid. 1) Copy this grid and figure «T» onto squared paper. 2) Draw the rotation of the figure «T». 3) Write the coordinates of the vertices of the rotated figure «T». Patterns Prepared by Knyazeva Alice and Dedova Daria Exercise Here are some patterns Try to draw your patterns, using: a) Rectangles b) Triangles c) Trapeziums CONSTRUCTING AND MEASURING Prepared by Lera Antonova-Rudzevich Gozh Marya CONSTRUCTING AND MEASURING There drawing tools are useful for constructing shapes. Constructing and measuring - in revealing the figure design features of the depicted object. Circles prepared by Dyatlov Dmitry and Dmitry Ovcharov Theory • Circle – the locus of points in the plane (all points), to which the distance from a given point called the center of the circle does not exceed the specified non-negative number, called the radius of the circle. • The segment connecting two points on the boundary of the circle and having its center, called the diameter of the circle. • The segment – part of a circle bounded by the arc and the chord subtending it. • The notion of a circle is a universal mathematical concepts, literally generalized to arbitrary metric spaces. However, some properties still remain: the bulge and the presence of central symmetry. practice Formulas: L=2πr C=pr² Exercises: R=10 π≈3 L≈? R=20 π≈3 C≈? R=5 π≈3,14 L≈? Try this L=6283 π≈3,1415926 π≈3,14 C≈28,2736 C=125660 π≈3,1415 r=2 r=6,2 r=3 π≈3,1415 r=? L≈? C≈? π≈? r=? Thank you for your attention!