• Given a line l and a point not on it, we use ‘equal alternate angles’ in a transversal diagram to draw a line parallel to l.
  • We also use the idea of ‘equal corresponding angles’ to do the construction.
  • Construction of Parallel Lines: Draw a line segment l and mark a point A not lying on it.
    • Take any point B on l and join B to A.
    • With B as centre and convenient radius, draw an arc cutting l at C and AB and D.
    • Now with A as centre and the same radius as in above step draw an arc EF cutting AB at G.
    • Place the metal point of the compasses at C and adjust the opening so that the pencil point is at D.
    • With the same opening as in above step and with G as centre draw another arc cutting the arc EF and H.
    • Now join AH and draw a line m.
  • Method of drawing a triangle, using indirectly the concept of congruence of triangles.
  • The following cases are used:
    • SSS: Given the three side lengths of a triangle.
    • SAS: Given the lengths of any two sides and the measure of the angle between these sides.
    • ASA: Two angles are given and the length of side included between then is given.
    • RHS: Given the length of hypotenuse of a right-angled triangle and the length of one of its legs.

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