Constructions of Triangles
Maharashtra Board · Class 9 · Mathematics
Quick revision notes for Constructions of Triangles — Maharashtra Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Previously Learned Constructions (Quick Recall)
- Construction when three sides are given (SSS)
- Construction when base and two adjacent angles are given (ASA)
- Construction when two sides and included angle are given (SAS)
Construction I: Base + Adjacent Angle + Sum of Remaining Sides
- Given: Base BC, angle adjacent to base (∠B), and sum AB + AC
- Strategy: Use perpendicular bisector property
- Key insight: If BD = AB + AC, then AD = AC (where D is on ray from B)
Construction II: Base + Adjacent Angle + Difference of Remaining Sides
- Given: Base BC, angle adjacent to base, and difference |AB - AC|
- Two cases: AB > AC or AC > AB
- Use perpendicular bisector property with modified approach
Construction III: Perimeter + Base Angles
- Given: Perimeter of triangle and two base angles
- Perimeter = AB + BC + AC
- Use angle bisector property for construction
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