- Let a line ‘l’ and a point P not lying on it be given.
- By using properties of a transversal and parallel lines, a line which passes through the point P and parallel to ‘l’, can be drawn.
- A triangle can be drawn if any one of the following sets of measurements are given :
- Three sides (SSS).
- Two sides and the angle between them (SAS).
- Two angles and a side (AAS) or (ASA).
- The hypotenuse and a leg in the case of a right-angled triangle (RHS).
- A figure has line symmetry, if there is a line about which the figure may be folded so that the two parts of the figure will coincide with each other.
- Regular polygons have equal sides and equal angles.
- They have multiple (i.e., more than one) lines of symmetry.
- Each regular polygon has as many lines of symmetry as it has sides.
- Mirror reflection leads to symmetry, under which the left-right orientation have to be taken care of.
- Rotation turns an object about a fixed point.
- This fixed point is called the centre of rotation.
- The angle by which the object rotates is the angle of rotation.
- Rotation may be clockwise or anti-clockwise.
- A half-turn means rotation by 180°. A quarter-turn means rotation by 90°.
- If, after a rotation, a figure or an object coincides with the original position, we say that it has a rotational symmetry.
- In a complete turn (of 360°), the number of times.
- The figure coincides with its original position is called its order of rotational symmetry.
- Every figure has a rotational symmetry of order 1 (i.e. a rotational symmetry of angle 360°).
- In such a case it is considered that the figure has no rotational symmetry.
- Some shapes have only one line of symmetry, like the letter E; some have only rotational symmetry, like the letter S; and some have both vertical and horizontal lines of symmetry, like the letter H.
- Plane figures are of two-dimensions (2-D) and the solid shapes are of three-dimensions (3-D).
- The corners of a solid shape are called its vertices, the line segments/ curves which form its skeleton are its edges and its flat surfaces are its faces.
- A net is a skeleton-outline of a solid that can be folded to make the solid.
- Solid shapes can be drawn on a flat surface.
- This is called a 2–D representation of a 3–D solid (shape).
- Two types of sketches of a solid are possible:
- An oblique sketch which does not have proportional measurements.
- An isometric sketch which is drawn on an isometric dot paper.
- In this sketch of the solid, the measurements are kept proportional.
- Different sections of a solid can be viewed in many ways:
- By cutting or slicing, the shape, which would result in the crosssection of the solid.
- By observing a 2-D shadow of a 3-D shape.
- By looking at the shape from different positions-the front-view, the side-view and the top-view.
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