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Geometrical Constructions Questions
1. Using a ruler and a pair of compasses only,
a) Construct a triangle ABC in which AB = 9cm, AC = 6cm and angle BAC = 37½^{0}
- Drop a perpendicular from C to meet AB at D. Measure CD and hence find the area of the triangle ABC
- Point E divides BC in the ratio 2:3. Using a ruler and Set Square only, determine point E. Measure AE.
2.
On the diagram, construct a circle to touch line AB at X and passes through the point C. (3 mks)
3. Using ruler and pair of compasses only for constructions in this question.
(a) Construct triangle ABC such that AB=AC=5.4cm and angle ABC=30^{0}. Measure BC (4 mks)
(b) On the diagram above, a point P is always on the same side of BC as A. Draw the
locus of P such that angle BAC is twice angle BPC (2 mks)
(c) Drop a perpendicular from A to meet BC at D. Measure AD (2 mks)
(d) Determine the locus Q on the same side of BC as A such that the area of triangle
BQC = 9.4cm^{2} (2 mks)
4. (a) Without using a protractor or set square, construct a triangle ABC in which AB = 4cm, BC = 6cm and ABC = 67½^{0}. Take AB as the base. (3mks)
Measure AC.
(b) Draw a triangle A^{1}BC^{1} which is indirectly congruent to triangle ABC. (3mks)
(c) Taking the mid point of AB as your centre of rotation (M). find the triangle A^{11}B^{11}C^{11} the image of A^{1}B^{1}C^{1} after -90^{0}. (4mks)
5. Construct triangle ABC in which AB = 4.4 cm, BC = 6.4 cm and AC = 7.4 cm. Construct an escribed circle opposite angle ACB (5 mks)
(a) Measure the radius of the circle (1 mk)
(b) Measure the acute angle subtended at the centre of the circle by AB (1 mk)
(c) A point P moves such that it is always outside the circle but within triangle AOB, where O is the centre of the escribed circle. Show by shading the region within which P lies. (3 mks)
6. (a) Using a ruler and a pair of compasses only, construct a parallelogram PQRS in which PQ = 8cm, QR = 6cm and PQR = 150^{0} (3 mks)
(b) Drop a perpendicular from S to meet PQ at B. Measure SB and hence calculate the area of the parallelogram. (5 mks)
(c) Mark a point A on BS produced such that the area of triangle APQ is equal to three quarters the area of the parallelogram (1 mk)
(d) Determine the height of the triangle. (1 mk)
7. Using a ruler and a pair of compasses only, construct triangle ABC in which AB = 6cm, BC = 8cm and angle ABC = 45^{o}. Drop a perpendicular from A to BC at M. Measure AM and AC
(4mks)
8. a) Using a ruler and a pair of compasses only to construct a trapezium ABCD
such that , ,and (5mks)
b)From the point D drop a perpendicular to the line AB to meet the line at E. measure DE hence calculate the area of the trapezium (5mks)
9. Using a pair of compasses and ruler only;
(a) Construct triangle ABC such that AB = 8cm, BC = 6cm and angle ABC = 30^{0}. (3 marks)
(b) Measure the length of AC (1 mark)
(c) Draw a circle that touches the vertices A,B and C. (2 marks)
(d) Measure the radius of the circle (1 mark)
(e) Hence or otherwise, calculate the area of the circle outside the triangle. (3 marks)
10. Using a ruler and a pair of compasses only, construct the locus of a point P such that angle APB = 60^{0} on the line AB = 5cm. (4mks)
11. Using a set square, ruler and pair of compases divide the given line into 5 equal portions. (3mks)
12. Using a ruler and a pair of compasses only, draw a parallelogram ABCD, such that angle DAB = 75^{0}. Length AB = 6.0cm and BC = 4.0cm from point D, drop a perpendicular to meet line AB at N
a) Measure length DN
b) Find the area of the parallelogram (10 mks)
13. Chebochok deposited shs.120,000 in a financial institution which offered a compound
interest at 8% p.a, compounded quarterly for 9 months. Find the accumulated amount by
the end of the period
14. 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
15. Without using a protractor, draw a triangle ABC where CAB = 30^{o}, AC = 3.5cm and
AB = 6cm. measure BC
16. (a) 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
(b) Drop a perpendicular from A to BC produced and measure its height
(c) Use your height in (b) to find the area of the triangle ABC
(d) Use construction to find the radius of an inscribed circle of triangle ABC
17. In this question use a pair of compasses and a ruler only
a) Construct triangle PQR such that PQ = 6 cm, QR = 8 cm and
b) Construct the height of triangle PQR in (a) above, taking QR as the base
18. 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)
(a) Construct BAC and mark point B
(b) Drop a perpendicular from B to meet the line AC at point F . Measure BF
19. Juma paid shs.450 for a trouser after getting a discount of 10%. The trader still made a
profit of 25% on the sale. What profit would the trader have made if no discount was allowed?
Geometrical constructions Answers
1 |
Area of AE= |
B_{1} B_{1} B_{1} B_{1} B_{1}
B_{1} M_{1} A_{1} B_{1} B_{1} |
conct 30^{0} conct 15^{0} AB 9cm AC 6cm ΔABC
CD
Loci of E For AE |
2 | B_{1}
B_{1}
B_{1} | construction of 90^{0}at x
bisection of line XC and location of centre O circle drawn | |
3 | |||
3 | B1 B1 B1 B1 B1
B1 B1 B1 B1 B1 | length AB = 5.4cm construction of 300 at B location of C and ABC length of BC stated identification of A as centre Locus of P drawn. (Bo if circle completed) dropping of perpendicular length AD stated his height locus of Q drawn | |
10 | |||
4. | B1 B1 B1 B1 B1 B1 B1
B1 B1 B1 | <67½0 constructed ABC complete AC = 5.7 0.1 C1Drawn A1Drawn A1BC1 completed Locating M (midpoint M of AB) B11 and A11 rotated C1 rotated A11B11C11 completed | |
10 |
6.
7. | AM = 4.2cm, AC = 5.6cm (±0.1cm) |
B1
B1
B1 |
Construction of 45^{o}
ΔABC
dropped from A to BC |
04 |
9. (a) Tan 60^{0} = AC
5cm M1
AC = 8.6605CM A1
(b) A = ½ x 5 x 8.6605 M1
A = 21.65125 A1
- ^{60}/_{360} x r^{2}
^{60}/_{360} x 3.142 x 25 M1
= 13.091cm^{2} A1
(d) Area of shaded part
Δ COA = Δ OBA, sector OCD = OCB
21.65 x 2 = 43.3025cm^{2} M1
13.091 x 2 = 26.182cm^{2} M1
Area of shaded part
43.3025 – 26.182 M1
= 17.11225cm^{2} A1
10
10. | Constant angle locus |
B1 B1
B1
B1 |
Const of 30^{0} at A Const. of 30^{0} at B
For one arc constructed
For lower arc constructed. | |||
11. |
B1
B1
B1 |
A line drawn slunt to touch the given line at one end.
Subdivided to 5 equal Sections
Parallel lines drawn from slunt line to touch the given line .All complete | ||||
03 | ||||||
12. |
a) length of ON = 3.9cm b) area = 6×3.9 = 23.4cm^{2} | B1 B1 B1 B1 B1 B1 B1 B1 B1 A1 | Both 90^{0} & 60^{0}at A 75^{0} at A 90^{0}&60^{0} at B 75^{0} drawn at point B Both AB=6cm and BC = 4cm Parallelogram completed drawn | |||
10 |
13. A = 120000 ( 1 + ^{8}/_{100} x ¼ )^{3}
120000 (1.02)^{3} = 127344.95
14.
15. BC = 3.5 cm + 0.1 B_{1}
_{ }B1 construction of ∠CAB.
B1 completion of triangle.
N/B/ Arcs should be seen in order to award the above marks.
16. Height = ± 8.7 1cm
( ½ x 7 x 8.7) 30.45cm^{2}
2 1cm
17. Give 1m of correct and complete triangle
Correct angle
Correct construction of the height
18.
19. Marked price = 100 x 450 = shs.500
90
Cost = 100 x 450 = shs.360
25
Profit = 500 – 360
= shs. 140