4.2 Geometrical Constructions

• Measuring angles with a protractor
• Bisecting angles using a ruler and a pair of compasses only
• Constructing 90°, 45°, 60° and 30° with ruler and compasses only
• Constructing 120°, 105° and other multiples of 7.5°
• Constructing triangles (SSS, SAS, ASA) with ruler and compasses only
• Constructing circles with ruler and compasses only
• Geometric constructions in Kenyan objects and patterns

• measure different angles in learning situations
• bisect angles using a ruler and a pair of compasses only in learning situations
• construct 90°, 45°, 60°, 30° and other angles that are multiples of 7.5° using a ruler and a pair of compasses only
• construct different triangles using a ruler and a pair of compasses only in different situations
• construct circles using a ruler and a pair of compasses only in different situations
• recognise use of geometric constructions of different shapes in objects

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

“Why do we use geometric constructions?”

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1. Measuring angles
   40 min · 1 practice tasks · quiz
   Place a protractor on the vertex, line up one arm with 0°, and read the other arm in degrees.
2. Bisecting an angle
   40 min · 1 practice tasks · quiz
   Split an angle into two equal parts using a ruler and a pair of compasses only.
3. Constructing 60 degrees
   40 min · 1 practice tasks · quiz
   Build an equilateral triangle on a ray so that one corner is a 60° angle, using ruler and compasses only.
4. Constructing 90 degrees
   40 min · 1 practice tasks · quiz
   Construct a perpendicular at a point on a line so the angle is 90°, using ruler and compasses only.
5. Constructing 30 and 45 degrees
   40 min · 1 practice tasks · quiz
   Bisect a constructed 60° to get 30°, and bisect a constructed 90° to get 45°.
6. Constructing 120 and 105 degrees
   40 min · 1 practice tasks · quiz
   Build 120° as the neighbour of 60° on a straight line, and 105° as 60° plus 45° at one vertex.
7. Multiples of 7.5 degrees
   40 min · 1 practice tasks · quiz
   Reach 7.5° by bisecting 15°, then combine 7.5° with 30°, 45° and 60° to make the other listed multiples.
8. Triangle given three sides
   40 min · 1 practice tasks · quiz
   Construct a triangle when all three sides are given (SSS) by drawing a base and swinging two arcs.
9. Triangle given two sides and the included angle
   40 min · 1 practice tasks · quiz
   Construct SAS: build the included angle first, then mark the two given lengths on its arms and join.
10. Triangle given two angles and a side
    40 min · 1 practice tasks · quiz
    Construct ASA: draw the given side, put a given angle at each end, and let the arms meet.
11. Constructing a circle
    40 min · 1 practice tasks · quiz
    Draw a circle with ruler and compasses from a centre and a radius, and mark a diameter through the centre.
12. Constructions in real life
    40 min · 1 practice tasks · quiz
    Recognise 90°, 60°, bisectors, triangles and circles in workshops, kitenge, pitches and badges, and say why we construct instead of guessing.