CBSE Class 7 Mathematics Practical Geometry Notes Set 09

Parallel Lines by Construction

A line parallel to a given line l through a point P can be drawn with a ruler and a set square by sliding the set square along the ruler. It can also be drawn with a compass by copying an angle: join P to a point B on l, then draw at P an angle equal to the angle that PB makes with l, so that the alternate interior angles are equal.
To draw a parallel at a given distance d, draw a perpendicular to the line, mark a point at distance d on it and draw a perpendicular to this perpendicular through that point.

When Can a Triangle Be Drawn?

A triangle needs three sides with the sum of any two greater than the third, or three angles that add to 180°. The data used to draw a unique triangle are: three sides (SSS), two sides and the included angle (SAS), two angles and the included side (ASA), or the hypotenuse and one side of a right triangle (RHS).

Steps for the Constructions

SSS: draw one side, cut arcs from its two ends with the other two side lengths and join the meeting point. SAS: draw one side, make the given angle at one end, mark the second side on the new ray and join. ASA: draw the side, make the two given angles at its ends and extend the rays until they meet.
RHS: draw the given leg, make a right angle at one end, and from the other end cut an arc equal to the hypotenuse on the perpendicular.

Worked Example

Is a triangle with sides 5 cm, 6 cm and 7 cm possible? Yes: 5 + 6 = 11 > 7, 5 + 7 = 12 > 6 and 6 + 7 = 13 > 5. Draw AB = 5 cm, an arc of 7 cm from A and an arc of 6 cm from B, and join their meeting point C to A and B.