1. Geometric Constructions
Unit 2 – Congruence
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Algebra 1 Institute

2. History Thales (600 BC) Hippocrates (440 BC) Euclid (300 BC)
In Golden Age of Greece, Greek mathematicians make a game of geometric constructions, using compass and straight edge alone.
Over the years, people have tried to find what they could and could not construct with only a compass and straight edge.
Euclid (300 BC)
Archimedes (220 BC)
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3. History Egyptian (1800 BC) Babylonian (3000 BC) Chinese (400BC) Indian
Ancient Egyptians used compass to mark off distance.
Over the years, people have tried to find what they could and could not construct with only a compass and straight edge.
Indian
(900 BC)
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4. How to make Geometric figures
Sketching/Drawing
By free hand
Or any tools
Put some pictures to illustrate
Compass-and-straight-edge Construction
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5. Warm up
Construct the following using pencil, compass and straight edge only.
Do not fold the paper!
3/4 unit ( 1 unit is given below)
Hints_1:
Hints_2:
Bisect a given angle
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6. Share with others Do you see different ways of construction? 3/4 unit
Bisect an angle
Hints_1:
Hints_2:
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7. Rules of Construction Euclid’s construction rule
Construction rules that are well accepted by modern society
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8. What are the advantages of applying Euclid’s Rule?
Open Discussion
What are the advantages of applying Euclid’s Rule?
When we use less tools to build geometric figures, we apply more geometric properties.
The compass method is usually more precise as it does not rely on the correct measurement of angles or lengths.
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9. Can we construct the following ?
Equilateral Triangle
Isosceles Triangle
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10. Find the center of a circle
If it is on a piece of paper…?
What if it is a steel ring…?
Can we copy a given triangle?
What if it is a steel disk…?
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11. Inscribed Regular Polygons
An inscribed equilateral hexagon
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12. Inscribed Regular Polygons
An inscribed equilateral triangle
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13. Inscribed Regular Polygons
An inscribed Square
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14. Inscribed Regular n-gons
Inscribed regular dodecagon
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15. Over Lapping The minor Arc CK= 1/3 of the circumference The minor arc
CF=1/4 of the Circumference
The minor arc
FK = 1/3 - 1/4
= 1/12 of the circumference
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16. Can we find a geometric length of any number using the unit of 1 ?
2 units
¾ unit …?
1/3
5/4
0.4
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17. Construction of Fractions
n=a/b
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18. Irrational Numbers
Hint_1:
Hint_2:
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19. Square root of any integer “n”
Beautiful?
Tedious?
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20. What if n is a large number?
Applying geometric mean
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21. Beauty of Geometric Construction
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22. Modern architectures and arts
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