Constructions Notes: Class 9 Maths Chapter 11
Class 9 Maths Chapter 11 Constructions covers the basic geometric constructions using a ruler and compass, including bisecting angles, constructing specific angles, and constructing triangles under given conditions.
Overview of Topics & Subtopics (Click to Jump)
1. Basic Constructions
Short Note:
• To bisect a given angle: draw arcs from the vertex cutting both arms, then arcs from those points to intersect; join the vertex to the intersection point.
• To construct the perpendicular bisector of a line segment: draw arcs of equal radius (more than half the segment) from both endpoints on either side; join the intersection points.
• To construct an angle of 60°: draw an arc from a point on a ray, then with the same radius draw an arc from that intersection; join the vertex to the new point.
• Angles of 30°, 90°, 45°, and 15° can be constructed by bisecting 60°, combining constructions, or bisecting a right angle.
2. Construction of Triangles
Short Note:
• Given base, a base angle, and sum of the other two sides: extend the base beyond the base angle by the given sum, join, then draw the perpendicular bisector to locate the third vertex.
• Given base, a base angle, and difference of the other two sides: similar method, marking off the difference along or beyond the base line and using a perpendicular bisector.
• Given perimeter and the two base angles: mark the full perimeter on a line, construct half the base angles at the ends, then use perpendicular bisectors to find the third vertex.