4.1 Geometrical Constructions

• Parallel and perpendicular lines
• Properties of polygons
• Irregular polygons
• Circles

• construct parallel and perpendicular lines in different situations
• divide a line proportionally in different situations
• identify angle properties of polygons in different situations
• construct regular polygons up to a hexagon in different situations
• construct irregular polygons up to a hexagon in different situations
• construct circles passing through the vertices of a triangle in different situations
• construct circles touching the sides of the triangle in different situations
• admire geometric patterns in objects and substances in real life

“How do we construct polygons?”

“Where do we use polygons in real-life situations?”

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1. Drawing parallel lines
   40 min · 1 practice tasks · quiz
   What parallel means, the set square and ruler method, and the compass method for a parallel through a given point.
2. Drawing perpendicular lines
   40 min · 1 practice tasks · quiz
   The perpendicular bisector of a segment, and the perpendicular from a point to a line.
3. Dividing a line proportionally
   40 min · 1 practice tasks · quiz
   Splitting a segment into equal parts, or in a given ratio, using a ray of equal steps and parallel lines.
4. Angles inside a polygon
   40 min · 1 practice tasks · quiz
   Splitting a polygon into triangles to get the interior angle sum, in degrees and in right angles.
5. Exterior angles and the number of sides
   40 min · 1 practice tasks · quiz
   Exterior angles always add to 360 degrees, which gives each angle of a regular polygon and lets you work back to the number of sides.
6. Constructing an equilateral triangle and a square
   40 min · 1 practice tasks · quiz
   The two simplest regular polygons, built from arcs and perpendiculars, and the 60 degree angle that comes free.
7. Constructing a regular pentagon
   40 min · 1 practice tasks · quiz
   Building a five-sided regular polygon inside a circle by stepping the central angle round with a protractor.
8. Constructing a regular hexagon
   40 min · 1 practice tasks · quiz
   Why the radius steps round a circle exactly six times, and the equilateral triangles that explains it.
9. Constructing irregular polygons
   40 min · 1 practice tasks · quiz
   Building a polygon from a list of given sides and angles, and checking it with the angle sum.
10. The circle through the vertices of a triangle
    40 min · 1 practice tasks · quiz
    Using perpendicular bisectors to find the one point equally far from all three corners, and drawing the circumscribed circle.
11. The circle touching the sides of a triangle
    40 min · 1 practice tasks · quiz
    Using angle bisectors to find the point equally far from all three sides, and drawing the inscribed circle.
12. Patterns with circles and polygons
    40 min · 1 practice tasks · quiz
    Building geometric patterns from the constructions learnt, and recognising them in Kenyan craft and building.