📌 Key Points
- Practical geometry uses compass and straightedge to construct exact geometric figures with precision.
- Perpendicular bisector of segment AB divides it into two equal parts and meets at 90°.
- Compass width for perpendicular bisector must be MORE than half the segment length.
- Perpendicular from point to line is constructed using equal arcs from two points on the line.
- Angle bisector divides an angle into two EQUAL parts using arcs of equal radius.
- An angle can be copied to a new location using compass without protractor.
- SSS (three sides), SAS (two sides and included angle), ASA (two angles and side), RHS (right angle) are valid triangle criteria.
- AAA and SSA are NOT valid triangle construction criteria (infinite or no unique solution).
- RHS criterion: right angle, hypotenuse, and one other side are given.
- Scale drawing is a proportional representation using scale factor.
- Scale 1:100 means 1 unit drawing = 100 same units actual (1 cm = 1 m).
- Actual distance = Drawing distance × Scale denominator.
- For scale drawing, multiply all actual dimensions by (1/scale denominator).
- Show all construction lines and arcs - examiners check method and accuracy.
- Compass should not be adjusted between related construction steps.
📘 Important Definitions
🔢 Formulas & Laws
Scale Calculation (Drawing to Actual)
Actual Distance = Drawing Distance × Scale Denominator
For scale 1:100, multiply drawing distance by 100 to get actual distance.
Scale Calculation (Actual to Drawing)
Drawing Distance = Actual Distance ÷ Scale Denominator
For scale 1:100, divide actual distance by 100 to get drawing distance.
Scale Conversion (Centimeters)
Scale 1:n means 1 cm = n cm actual = (n/100) m
For scale 1:100, 1 cm = 100 cm = 1 m actual.
Scale Conversion (Distance)
Scale 1:n means 1 mm = n mm actual; 1 cm = n cm actual
Apply same multiplier to any unit of measurement.
Area Relationship in Scale
If scale is 1:n, then area scale is 1:n²
Scale 1:100 gives area scale 1:10,000 (1 cm² = 10,000 cm² = 1 m²).
⚠️ Common Mistakes
✗ Wrong: Using compass width less than or equal to half the segment for perpendicular bisector
✓ Correct: Always use compass width GREATER than half the segment to ensure arcs intersect.
✗ Wrong: Adjusting compass between steps when constructing perpendicular bisector
✓ Correct: Once set, keep compass at same width throughout the construction.
✗ Wrong: Using unequal arc radii when bisecting an angle
✓ Correct: Both arcs (from angle arms and from points P and Q) must have equal radii.
✗ Wrong: Using AAA criterion to construct triangle
✓ Correct: AAA does not uniquely determine a triangle. Always need at least one side.
✗ Wrong: Forgetting to apply scale factor when converting between drawing and actual
✓ Correct: Always multiply or divide by scale denominator consistently.
✗ Wrong: Using scale factor in wrong direction (actual/drawing instead of drawing/actual)
✓ Correct: Scale 1:100 means divide by 100 to draw, multiply by 100 to find actual.
📝 Exam Focus
These questions are frequently asked in CBSE exams:
🎯 Last-Minute Recall
Close your eyes and try to recall: Key definitions, formulas, and 3 common mistakes. If you can recall 80% without looking, you're exam-ready!