These comprehensive RBSE Class 9 Maths Notes Chapter 11 Constructions will give a brief overview of all the concepts.
RBSE Class 9 Maths Chapter 11 Constructions
1. A geometrical construction is the process of drawing a geometrical figure using only two instruments; an ungraduated rular and compass.
2. A line which divides the given line in two equal parts and is perpendicular to the line segment is called the perpendicular bisector.
3. Angles, lines and points in one figure which bear a similar relationship, each to each, to angles, fines and points to another figure.
4. Firstly, draw a rough diagram of the geometrical shape with a dark pencil and mark all the given measurements.
5. As far as possible 60°, 120°, 90°, 105°, 45°, 135° and 150° angles are made with the help of compass and ruler while all other angles are drawn using a protractor.
6. Construction of triangles is generally done in the following manner :
(i) Construction of a triangle whose three sides are given.
(ii) Construction of a triangle whose two sides and angles between them is given.
(iii) Construction of a triangle whose one side and two angles are given.
(iv) Construction of a right-angled triangle in which hypotenuse and one other side is given.
(v) Construction of a triangle whose two sides and an angle opposite to one of the given sides is given.
7. Construction of triangle is not possible if only the following components of triangle are known-
(i) Three angles : Construction of triangle is not possible if all three angles are given.
(ii) If two sides and their one opposite acute angle is given, then construction of triangle leads to ambiguous situation.
8. To construct a triangle given its base, a base angle and sum of the other two sides.
9. To construct a triangle given its base, a base angle and the difference of the other two sides.
10. To construct a triangle given its perimeter and its two base angles.