File size: 1,917 Bytes
8c52ce6 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | ---
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. |