source: ncert
topic: geometry
class_level: class_9
chapter: ch11
difficulty: intermediate
Class 9 | Ch11: Constructions BASIC CONSTRUCTIONS (Class 6 review): Perpendicular bisector, angle bisector, 60°, 90°, 45°, 30° using compass. CLASS 9 CONSTRUCTIONS: Construction 1: Angle of 60° (without protractor). Draw ray OA. Arc from O cuts OA at P. Same radius arc from P cuts first arc at Q. Angle QOP=60°. Construction 2: Bisect any given angle. Construction 3: Draw perpendicular to given line from given point. Construction 4: Construct triangle given base, base angle, and sum of other two sides. Steps: Draw BC (base). Draw angle at B. Mark D on ray such that BD=AB+AC. Join DC. Bisect DC to get perpendicular bisector meeting BD at A. Join AC. Triangle ABC is constructed. Construction 5: Construct triangle given base, base angle, and DIFFERENCE of other two sides. Two cases: given side longer or shorter. Construction 6: Construct triangle given perimeter and two base angles. Steps: Draw line XY=perimeter. Draw angles at X and Y. Bisect both angles. Bisectors meet at A. Draw perpendicular bisectors of XA and YA to get B and C. Triangle ABC is the required triangle. Construction 7: Construct right triangle given hypotenuse and one side. JUSTIFICATION OF CONSTRUCTIONS: Each construction must be justified by proving why the constructed figure satisfies given conditions. SOLVED EXAMPLES: Example 1: Construct triangle with perimeter 11cm and base angles 60° and 45°. Step 1: Draw XY=11cm. Step 2: Draw 60° at X, 45° at Y. Step 3: Bisect these angles. Bisectors meet at A. Step 4: Perpendicular bisectors of XA and YA meet XY at B and C respectively. Triangle ABC has perimeter 11cm and base angles 60° and 45°. COMMON MISTAKES: Always bisect the BASE angles at X and Y (not the constructed angles). In construction 4: bisect DC (the line joining end of ray to far end), not the base BC.