Form 1 Mathematics
Using a ruler and a pair of compass only, construct a rhombus PQRS such that PQ = 6cm and SPQ = 75°.
Measure the length of PR.
answer
Form 1 Mathematics
(a) Using a ruler and a pair of compasses only, construct:
(i) a parallelogram ABCD, with line AB below as part of it, such that AD = 7 cm and angle BAD = 60°; 
(ii) the locus of points equidistant from AB and AD;
(iii) the perpendicular bisector of BC. (b) (i) Mark the point P that lies on DC and is equidistant from AB and AD. (ii) Measure BP. (c) Describe the locus that the perpendicular bisector of BC represents. (d) Calculate the area of trapezium ABCP.
answers
Form 1 Mathematics
(a) Using a ruler and a pair of compasses only, construct a quadrilateral PQRS in which PQ = 5 cm, PS = 3 cm, QR = 4 cm, PQR = 135° and SPQ is a right angle.
(b) The quadrilateral PQRS represents a plot of land drawn to a scale of l:4000. Determine the actual length of RS in metres.
answer
Form 1 Mathematics
Using a ruler and a pair of compasses only, construct:
(a) a triangle LMN in which LM = 5 cm, LN = 5.6 cm and MLN = 45° (b) the circle that touches all the sides of the triangle.
answer
Form 1 Mathematics
Using a pair of compasses and ruler only, construct
a)i)Triangle ABC in which AB= 5 cm, <BAC=30 and <ABC = 105. ii)A circle that passes through he vertices of the triangle ABC. Measure the radius iii)the height of triangle ABC with AB as the base. Measure the height b) Determine the area of circle that lies outside the triangle correct to 2 decimal places
answers
Form 1 Mathematics
The figure below is a triangle XYZ. Using a pair of compasses and a ruler only, construct an inscribed circle such that the centre of the circle and the point x are the opposite sides of line Yz.
Answer
Form 1 Mathematics
Line AB drawn below is a side of a triangle ABC.
(a) Using a pair of compasses and ruler only construct: (i) triangle ABC in which BC = 10cm and angle CAB = 90°; (ii) a rhombus BCDE such that angle CBE = 120°; (iii) a perpendicular from F, the point of intersection of the diagonals of the rhombus, to meet BE at G. Measure FG; (iv) a circle to touch all the sides of the rhombus. b) Determine the area of the region in the rhombus that lies outside the circle
ANSWERS
Form 1 Mathematics
Point C divide line AB given below externally in the ratio 5:2
By construction, determine the position of point c
Answer
Form 1 Mathematics
Using a pair of compasses and a ruler only, construct
(a) (i) Triangle ABC in which AB =5cm, ˂BAC = 300 and ˂ABC = 1050 (ii) A circle that passes through the vertices of the triangle ABC. Measure the radius (iii) The height of triangle ABC WITH AB as the base. Measure the height (b) Determine the area of the circle that lies outside the triangle correct to 2decimal places
answers
Form 1 Mathematics
(a) Using a pair of compasses and ruler only, construct an escribed circle to touch side XZ of triangle XYZ drawn below
(b) Measure the radius of the circle
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Form 1 Mathematics
(a) on the same diagram construct:
(i) triangle ABC such that AB = 9 cm, AC= 7 cm and angle CAB = 60°; (ii) the locus of a point P such that P is equidistant from A and B; (iii) the locus of a point Q such that CQ ≤ 3.5cm. (b) On the diagram in part (a): (i) shade the region R, containing all the points enclosed by the locus of P and the locus of Q, such that AP ≥ BP; (ii) find the area of the region shaded in part (b)(i) above.
answers
Form 1 Mathematics
Using a ruler and a pair of compasses only.
a) Construct triangle ABC in which BC = 8cm, angle ABC = 1050 and BAC =450
b) Drop a perpendicular from A to meet CB produced at p. Hence find the area of triangle ABC.
aNSWER
Form 1 Mathematics
Construct a circle centre x and radius 2.5 cm. Construct a tangent from a point P, 6 cm from x to touch the circle at R. Measure the length PR.
answer
Form 1 Mathematics
Using a pair of compasses and ruler only, construct a quadrilateral ABCD in which AB = 4cm, BC = 6 cm, AD = 3 cm, angle ABC = 135° and angle
DAB = 60°. Measure the size of angle BCD.
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Form 1 Mathematics
(a) In the figure below, lines NA and NB represent tangents to a circle at points A and B.
Use a pair of compasses and ruler only to construct the circle. 
(b) Measure the radius of the circle.
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Form 1 Mathematics
Using a ruler and a pair of compases only:
(a) construct a parallelogram PQRS in which PQ = 6 cm, QR = 4 cm and angle SPQ= 75°; (b) determine the perpendicular distance between PQ and SR.
answers
Form 1 Mathematics
(a) Using line AB given below, construct the locus of a point P such that angle APB 90.
(b) On the same diagram locate two possible positions of point C such that point C is on the locus of P and is equidistant from A and B.
answer
Form 1 Mathematics
Using a ruler and a pair of compasses only, construct a rhombus QRST in which angle TQR = 600 and QS = 10 cm.
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Form 1 Mathematics
In the figure below, O is the centre of the circle and radius ON is perpendicular to the line TS at N.
Using a ruler and a pair o compasses only, construct a triangle ABC to inscribe the circle, given that angle ABC = 600, BC = 12 cm and points B and C are on the line TS
answer
Form 1 Mathematics
The diagonals of a rhombus PQRS intersect at T. Given that p(2,2), Q(3, 6 ) and R(-1, 5):
a) Draw the rhombus PQRS on the grid provided; b) State the coordinates of T.
answer
Form 1 Mathematics
Line AB shown below is a side of a trapezium ABCD in which angle ABC in which angle ABC= 1050, BC = 4 cm,CD = 5 cm and CD is parallel to AB.
Using a ruler and a pair of compasses only:
a) Complete the trapezium; b) Locate point t on line AB such that angle ATD = 900
answer
Form 1 Mathematics
Line AB given below is one side of triangle ABC. Using a ruler and a pair of compasses only;
(i) Complete the triangle ABC such that BC=5cm and angle ABC=45
(ii) On the same diagram construct a circle touching sides AC,BA produced and BC produced.
answer
Form 1 Mathematics
Line BC below is a side of a triangle ABC and also a side of a parallelogram BCDE.
Using a ruler and a pair of compasses only construct:
(i) The triangle ABC given that angle ABC = 1200 and AB= 6cm (ii) The parallelogram BCDE whose area is equal to that of the triangle ABC and point E is on line AB
answer
Related Questions and Answers on Geometric ConstructionsForm 1 Mathematics
In this question use a ruler and a pair of compasses
Line PQ drawn below is part of a triangle PQR. Construct the triangle PQR in which
a) < QPR = 300 and line PR = 8cm 
b) On the same diagram construct triangle PRS such that points S and Q are no the opposite sides of PR<PS = PS and QS = 8cm c) A point T is on the a line passing through R and parallel to QS.If <QTS =900, locate possible positions of T and label them T1 and T2, Measure the length of T1T2.
Answer
Form 1 Mathematics
The figure below shows a triangle ABC.
Answer
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