Important Formulas: Playing with Constructions | Mathematics for Class 6 PDF Download

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1. Drawing with Compass:

• A compass is used to draw circles and curves.
• To draw a circle, mark a point 'P', and place other points that are 4 cm away from 'P'.
• All points that are 4 cm away from the center 'P' form a circle.
• The distance from the center 'P' to any point on the circle is called the radius.
  

2. Constructing Figures:

• A person or figure can be drawn with a compass by placing the tip at specific points and setting the correct radius.
• A wavy pattern can be drawn as a sequence of half circles, taking the central line (like AB = 8 cm) as the base.
• Adjust the compass radius to make uniform waves along the line.
  

3. Properties of Squares and Rectangles:

• Rectangle:
  1. Opposite sides are equal in length.
  2. All angles are 90°.
     
• Square:
  1. All sides are equal in length.
  2. All angles are 90°.
     
• Rotating squares or rectangles doesn’t change their properties.

4. Constructing Squares and Rectangles:

• A square with side lengths (e.g., 6 cm) can be drawn by marking a perpendicular line from one side and measuring the length of each side.
• A rectangle can be constructed by measuring and marking the lengths of opposite sides and checking if the angles are 90°.
  Construction of Square

5. Exploring Distance between Points on Rectangles:

• Points 'X' and 'Y' can be placed along the sides of a rectangle to measure distances.
• The minimum distance between 'X' and 'Y' occurs when they are closest on the sides.
• The maximum distance between 'X' and 'Y' occurs when they are farthest, typically along the diagonal.

6. Breaking Rectangles into Squares:

• A rectangle can be divided into identical squares.
• This can be planned by visualizing or drawing a rough sketch to understand how the rectangle is split.