| --- |
| source: ncert |
| topic: geometry |
| class_level: class_9 |
| chapter: ch11 |
| difficulty: intermediate |
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| |
| 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. |
