## PRACTICAL GEOMETRY- ESSENTIAL POINTS

• 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.