Geometrical Constructions Questions and Answers - Form 1 Topical Mathematics

Questions

1. Using a ruler and a pair of compasses only,
   1. Construct a triangle ABC in which AB = 9cm, AC = 6cm and angle BAC = 37½^o
   2. Drop a perpendicular from C to meet AB at D. Measure CD and hence find the area of the triangle ABC
   3. Point E divides BC in the ratio 2:3. Using a ruler and Set Square only, determine point E. Measure AE.
2. Using a ruler and a pair of compasses only, draw a parallelogram ABCD in which AB = 6cm, BC = 4cm and angle BAD = 60^o. By construction, determine the perpendicular distance between the lines AB and CD.
3. Without using a protractor, draw a triangle ABC where <CAB = 30^o, AC = 3.5cm and
   AB = 6cm. measure BC.
4.  
   1. Using a ruler and a pair of compass only, construct a triangle ABC in which
      angle ABC =37.5^o, BC =7cm and BA = 14cm
   2. Drop a perpendicular from A to BC produced and measure its height
   3. Use your height in (b) to find the area of the triangle ABC
   4. Use construction to find the radius of an inscribed circle of triangle ABC
5. In this question use a pair of compasses and a ruler only
   1. Construct triangle PQR such that PQ = 6 cm, QR = 8 cm and <PQR = 135°
   2. Construct the height of triangle PQR in (a) above, taking QR as the base
6. On the line AC shown below, point B lies above the line such that <BAC = 52.5^o and AB = 4.2cm. (Use a ruler and a pair of compasses for this question)
   1. Construct <BAC and mark point B
   2. Drop a perpendicular from B to meet the line AC at point F. Measure BF

Answers

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   BC = 3.5 cm + 0.1 B1
   B1 construction of ∠CAB.
   B1 completion of triangle.
   N/B/ Arcs should be seen in order to award the above marks.

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