Embedded Files
Scale Drawings
Key Concepts
A scale drawing is a diagram or plan that represents an object or layout proportionally reduced or enlarged
Common in maps, architectural plans, and technical diagrams
Scale is written as a ratio: → e.g. 1 : 100 means 1 unit on the drawing = 100 units in real life
How to Work with Scale Drawings
Identify the scale used in the drawing (e.g. 1 cm : 5 m)
Convert real measurements to scaled values using the ratio
Use a ruler to draw accurate lengths based on the scale
Label all dimensions clearly
Example:
A room is 4 m × 3 m. Scale = 1 : 100
Convert to cm: 4 m = 400 cm → 400 ÷ 100 = 4 cm
3 m = 300 cm → 300 ÷ 100 = 3 cm
Draw a rectangle 4 cm × 3 cm
Bearings in Scale Drawings
Bearings are measured clockwise from north (000°)
Always given as three-digit angles (e.g. 045°, 120°, 270°)
Used to describe direction between points
Example:
If the bearing of B from A is 045°, then B lies northeast of A
Image Credits: CK-12 Foundation, cimt,
Similarity
Key Concepts
Similar shapes have:
The same shape but different sizes
Equal corresponding angles
Sides in proportion (i.e. same scale factor)
Scale factor is the ratio of corresponding sides: → Scale factor = (length in image) ÷ (length in original)
If scale factor k > 1, the shape is enlarged
If scale factor 0 < k < 1, the shape is reduced
Example 1: Finding a Missing Side
Two similar triangles have sides:
Triangle A: 3 cm, 4 cm, 5 cm
Triangle B: 6 cm, 8 cm, ?
→ Scale factor = 6 ÷ 3 = 2 → Missing side = 5 × 2 = 10 cm
Triangle B has sides: 6 cm, 8 cm, 10 cm
Example 2: Using Scale Factor to Compare Areas
If two shapes are similar with scale factor k, then:
Area scale factor = k²
So if the scale factor = 3 → Area of larger shape = (Area of smaller shape) × 3² = (Area of smaller shape) × 9
Example 3: Using Scale Factor to Compare Volumes
If two solids are similar with scale factor k, then:
Volume scale factor = k³
Example: Scale factor = 2 → Volume of larger solid = (Volume of smaller solid) × 2³ = (Volume of smaller solid) × 8
Symmetry
Key Concepts
Line symmetry (reflectional symmetry): A shape has line symmetry if it can be folded along a line so that both halves match exactly. → The line is called the line of symmetry
Rotational symmetry: A shape has rotational symmetry if it can be rotated (less than a full turn) and still look the same. → The number of times it matches in one full turn is called the order of rotational symmetry
Symmetry in Polygons
Regular polygons (equal sides and angles) have:
n lines of symmetry and rotational symmetry of order n, where n = number of sides
Example:
A regular hexagon has 6 sides → 6 lines of symmetry → Rotational symmetry of order 6
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