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New Syllabus Mathematics Book 1 7th Edition Teh Keng Seng, Loh Cheng Yee, Joseph Yeo, Ivy Chow - Solutions

Construct a rhombus ABCD such that AB = 6 cm and A hat BC = 115 deg . Measure and write down the length of each of the two diagonals.
Construct a rectangle of sides 96 mm and 84 mm. Measure and write down the length of each of the two diagonals.
Construct a parallelogram ABCD such that AB = 10cm BC = 12cm and A hat BC = 80 deg . Measure and write down the length of the diagonal BD.
Construct a quadrilateral PQRS such that PQ = 6.5 cm, QR=4.8 cm, RS=8.5 cm, PQR = 75 and QRS = 98. (i) Measure and write down the length of PS. (ii) Measure and write down the size of PSR.
Construct a circle of any radius. Label the centre of the circle as O.(i) A chord of a circle is a line segment such that its end points lie on the circumference of the circle. A chord that passes through the centre of the circle is known as the diameter of the circle. Draw a chord in your circle
Construct APQR such that PQ = 8.3cm PR = 9.2cm and QR = 7.9cm The point 7 is such that it is equidistant from PQ, PR and QR. Find and label T.
Construct AABC such that AR = 8.5cm AC = 4.6cm and B hat AC = 54 deg , The point S is such that it is equidistant from A, B and C. Find and label S.
Construct AABC such that AB = 10.2cm AC = 11 cm and B hat AC = 62 deg .(i) Measure and write down the length of BC.(ii) Construct a circle of radius 5 cm with its centre at C.(iii) Construct the angle bisector of ACB such that it cuts the circle at S inside the triangle and AB at T. Measure and
13. Construct AXYZ such that XY = 8cm X hat YZ = 49 deg and Y hat XZ = 74 deg .(i) Construct the perpendicular bisector of XY.(ii) Construct the angle bisector of XYZ.(iii) These two bisectors intersect at U.Complete the following statement:The point U is equidistant from the points from the lines
Construct AXYZ such that XY = 8cm X hat YZ = 55 deg and gamma hat xz = 64 deg .(i) Measure and write down the length of XZ.(ii) Construct the perpendicular bisector of YZ such that it cuts XY. Measure and write down the length of UY, such that U is the point where the perpendicular bisector of YZ
Construct APQR such that PQ = 8.8cm PR = 9.2cm and QR = 10.4cm(i) Measure and write down the size of the angle facing the longest side.(ii) Construct the angle bisector of POR such that it cuts PR. Measure and write down the length of PT, such that T is the point where the angle bisector of POR
Construct AABC such that AB = 9.8cm BC = 6.5cm and A hat BC = 88 deg(i) Measure and write down the length of AC.(ii) Construct the perpendicular bisector of AB such that it cuts AC. Measure and write down the length of BS, such that S is the point where the perpendicular bisector of AB cuts AC.
Construct AXYZ such that XY = 10.2cm X hat YZ = 60 deg and gamma hat Xz = 45 deg Measure and write down the length of XZ.
Construct an equilateral triangle with sides 9.5 cm each.
Construct APQR such that PQ = 9.5cm PR = 8.5cm and QR = 9.8cm(i) Measure and write down the size of the angle facing the shortest side.(ii) Construct the perpendicular bisector of QR such that it cuts PQ. Measure and write down the length of QT, such that T is the point where the perpendicular
9. Construct AABC such that AB = 9.4cm AC = 8.8 cm and A hat BC = 60 deg .(i) Measure and write down the size of the angle facing the shortest side.(ii) Construct the angle bisector of BẬC such that it cuts BC. Measure and write down the length of CS, such that S is the point where the angle
Construct an isosceles triangle PQR such that PQ = PR = 10cm and QR = 9cm Measure and write down the size of QPR.
Construct AABC such that AB = 5cm BC = 9cm and B hat AC = 90 deg . Measure and write down the length of AC.
Construct AABC such that AB = 8cm BC = 6.5cm and ABC 80. Measure and write down the length of AC.
Draw an angle BAC of 56. Construct the angle bisector of BẬC.
Draw a line segment AB of length 9.5 cm. Construct the perpendicular bisector of AB.
Construct AXYZ such that XY = 9 cm, X hat YZ = 38 deg and YXZ=67".(i) Construct the perpendicular bisector of XZ.(ii) Construct the angle bisector of XZY.(iii) The two bisectors intersect at U.Complete the following statement:The point U is equidistant from the points and and equidistant from the
Construct APQR such that PQ = 8.4 cm, PR = 7.2 cm and QR = 9.8 cm.(i) Measure and write down the size of the angle facing the longest side.(ii) Construct the angle bisector of QPR such that it cuts QR.Measure and write down the length of QT, such that T is the point where the angle bisector of QPR
Construct APQR such that PQ = 10.5cm PR = 8.5 cm and QR = 9.5cm(i) Measure and write down the size of the angle facing the longest side(ii) Construct the angle bisector of QPR such that it cuts QR. Measure and write down the length of QT, such that T is the point where the angle bisector of QPR
Construct AABC such that AB = 7.6 cm, BC = 4.8 cm and A hat BC = 130 deg(i) Measure and write down the length of AC.(ii) Construct the perpendicular bisector of AB such that it cuts AC. Measure and write down the length of BS, such that S is the point where the perpendicular bisector of AB cuts AC.
Construct AABC such that AB = 10.5 cm, BC = 7.5 cm and A hat BC = 60 deg .(i) Measure and write down the length of AC.( ii) Construct the perpendicular bisector of AB such that it cuts AC.Measure and write down the length of BS, such that S is the point where the perpendicular bisector of AB cuts
Draw an angle BAC of 66". Construct the angle bisector of BC. A 66 arc 2 R arc 1 P B
Find a formula for the number of diagonals of an n-sided polygon.
(i) How do you define an exterior angle of a concave polygon?(ii) The sum of exterior angles of any convex n-gon is 360°. Is the sum of exterior angles of a concave n-gon also 360°? Explain your answer.
The sum of interior angles of a convex i-gon is (n-2) x 180". Does this formula apply to the sum of interior angles of a concave n-gon? Explain your answer.
In the figure, AABC is an isosceles triangle in which AB = AC and BC = 20. If CBF = 50 and BCD = 60, find CDF. A D 20 50" 66) B C
In the figure, AABC is an isosceles triangle in which AB = AC and BC = 20. If AD = BC, find ADB. B 20 C
If the sum of the interior angles of an u-sided polygon is four times the sum of its exterior angles, find the value of n.
The ratio of an interior angle to an exterior angle of an a-sided regular polygon is 13:2. Find the value of n.
Two of the exterior angles of an n-sided polygon are 35 and 72", and the remaining exterior angles are 23" each. Find the value of n.
The ratio of the interior angles of a pentagon is 3:4:5:5:7. Find(i) the largest interior angle,(ii) the largest exterior angle.
One of the interior angles of an n-sided polygon is 126" and the remaining interior angles are 162" each. Find the value of n.
8. The sum of interior angles of a polygon with (2n 3) sides is equal to 62 right angles. Find the value of 1.
The figure shows a square ABCD and an equilateral triangle ABE. Find CD. D. C B
The figure shows a kite ABCD where AB = AD, BC = CD, ABD = 62 and BCD=118". Find (i) BD, (ii) BDC. B 62 D 118 C
The figure shows a parallelogram ABCD where ABC = 108 and BAC = 40. Find (i) AD, (ii) CD. D 40 108 B
Find the value(s) of the unknown(s) in each of the following figures. (a) D H 62 95 (b) LK bbb D 114 112 F B 4b H B 36
Given that AB // DC, find the value(s) of the unknown(s) in each of the following figures. (a) D ++ A " B (b) D P76 E d 118 (c) B A C 58 B
The figure shows the internal structure of a beehive made up of regular hexagonal cells that can form tessellations with no overlaps or gaps. (i) Name another two regular polygons that can form tessellations and sketch their tessellations. (ii) Why are these regular polygons able to form
The figure shows part of an n-sided polygon where each side is produced. a,, a and a are the interior angles of the polygon and x, xxx, and x are its exterior angles. Show that the sum of exterior angles of the polygon is 360, i.e. x, +x+x+x+ = 360 +X_
In the figure, ABCDEF is part of an -sided regular polygon. Each exterior angle of this polygon is 36". Find (i) the value of n, (ii) BDE, (iii) CD. C D E
14. In the figure, ABCDE is part of an n-sided regular polygon. The ratio of an interior angle to an exterior angle of this polygon is 5: 1. Find (i) the value of n, (ii) ACD, (iii) ADE. D
1 In the figure, AFJD, AGHC, BGFE, BHID and CIJE are straight lines.Find La + Lb + Lc + Ld + Le. A 8-14 E- F H D 2.
16. In the figure, ACJL, BCEF, DEGH and IGJK are straight lines.Find Za + b + Lc + Ld + Le + LS + Lg + Lh. B F H A
The exterior angles of a triangle are 3y, 4y and 5y.(i) Find the value of y.(ii) Find the smallest interior angle of the triangle.
If the sizes of the interior angles of a pentagon are 2x", 3x, 4x", 5x and 6x", find the largest interior angle of the pentagon.
6. Find the number of sides of a regular polygon if each interior angle of the polygon is(a) 140,(b) 162",(c) 172,(d) 175"
In the figure, ABCDE is a regular pentagon and ABPQRS is a regular hexagon. X is the centre of the hexagon. 04 Find (i) ABP, (ii) PX, R (iii) AXB. (iv) ABC, (v) AD, (vi) ASE. B
The points A, B, C and D are consecutive vertices of a regular polygon with 20 sides. Find(i) ABC,(ii) ABD.
ABCDEFG is a regular heptagon. If AB and DC are produced to meet at H, find the value of BHC.
Three of the exterior angles of an n-sided polygon are 50 each, two of its interior angles are 127 and 135°, and the remaining interior angles are 173" each. Find the value of n.
Three of the exterior angles of an n-sided polygon are 15°, 25 and 70", and the remaining exterior angles are 50° each. Find the value of n.
Find the number of sides of a regular polygon if each exterior angle of the polygon is(a) 90°,(b) 45°,(c) 12",(d) 4".
(a) By finding the size of each exterior angle of a regular polygon with 24 sides, calculate the size of each interior angle of the polygon.(b) By finding the size of each exterior angle of a regular polygon with 36 sides, calculate the size of each interior angle of the polygon.
3. (a) (i) Find the sum of interior angles of a regular hexagon.(ii) Hence, find the size of each interior angle of a regular hexagon.(b) (i) Find the sum of interior angles of a regular polygon with 18 sides.(ii) Hence, find the size of each interior angle of a regular polygon with 18 sides.
Find the value of the unknown in each of the following figures. (a) D (b) 78 62" (c) E 101 20 38" 152" B (d) 84 2b" 78 B 108" D ta F4d Ad C 102' 5df A B
Find the sum of the interior angles of each of the following polygons.(a) 11-gon(b) 12-gon(c) 15-gon(d) 20-gon
In the figure, ABCDE is part of an n-sided regular polygon, BPQRC is a regular pentagon and CRSD is a square. P D E Find (i) PBC, (ii) QCR, (iii) BCD, (iv) BDC, (v) the value of n. R S
ABCDE is a regular pentagon. If AB and DC are produced to meet at F, find the value of BFC.
Two of the exterior angles of an -sided polygon are 25 and 26", three of its interior angles are 161 each and the remaining interior angles are 159" each. Find the value of n.
By finding the size of each exterior angle of a regular decagon, find the size of each interior angle of the decagon.Note: Refer to Worked Example 7. This is another method to find the size of each interior angle of a regular polygon.
Find the number of sides of a regular polygon if(a) each exterior angle of the polygon is 40",(b) each interior angle of the polygon is 178".
Calculate the number of sides of a regular polygon if (a) each exterior angle of the polygon is 24, (b) each interior angle of the polygon is 162.
Is it possible for a regular polygon to be a concave polygon? Explain your answer.
(i) Is it possible for a regular polygon to have an exterior angle of 70? Explain your answer(ii) If an exterior angle of a regular polygon is an integer, what are all the possible values of the angle?
What do you think is the sum of the exterior angles of a pentagon? Explain your answer.
1. The template shows a pentagon with 5 exterior angles. Click on the point 'Drag me towards o' and drag it until it reaches O. Fig. 11.20 shows the figure just before the point reaches O. Sum of Exterior Angles of Polygon Exterior angles are coloured yellow Drag me towards O
We can design figures of different shapes which tessellate In each of the diagrams below, we start with a simple design. Then, we remove a piece from a corner and add it onto the opposite side and we will have a new figure which tessellates. Create a few new tessellating patterns on your own in
Which of the following figures will tessellate? (a) Isosceles triangle (c) 1 (e) Scalene trapezium (No sides equal) Circle (b) (d) (f) Scalene triangle kite Quadrilateral
4. Find out whether rhombuses, regular octagons and regular decagons tessellate. We can also tessellate irregular polygons. A tessellation formed by parallelograms. A tessellation formed by isosceles trapeziums (two sides equal).
(i) Find the sum of interior angles of a regular polygon with 24 sides. (ii) Hence, find the size of each interior angle of a regular polygon with 24 sides.
(i) Calculate the sum of interior angles of a regular decagon. (ii) Hence, calculate the size of each interior angle of a regular decagon.
Find the value of b in the figure. D E 114 128 122 36 th A B
Find the value of a in the figure. F 117 121 B
In a kite PQRS, PQ QR, PS = RS, Q hat PR = 42 deg and P hat SR = 64 deg . Find(i) PRS,(ii) PQR.
In a trapezium ABCD, AB // DC, AB = AD, BCD=52" and ADC = 62". Find(i) ABD,(ii) CBD.
In a rhombus WXYZ, W hat XY = 108 deg Find(i) XŻY,(ii) XYZ,(iii) XWY.
In a parallelogram PQRS, Q hat PR = 42 deg and Q hat RS = 70 deg .Find(i) PQR,(ii) PRQ.
In a rectangle ABCD, E is the midpoint of AB and CED = 118. Find(i) ADE,(ii) DĈE.
The figure shows a kite ABCD where AB = AD, BC = CD and the diagonals AC and BD intersect at E. Find (i) ABD, (ii) CBD. 25 D +47 C E B
The figure shows a trapezium ABCD where AB // DC. Find the value of x and of y. A D 5.x C 2.2x B
The figure shows a rhombus ABCD where the diagonals AC and BD intersect at E. Find the value of x. (3x+7)" A E (2x+53) B
The figure shows a rhombus ABCD. The diagonal DB is produced to E such that BC = BE and CDE = 46*. Find (i) BD, (ii) BE. A D 46 C B E
The figure shows a parallelogram ABCD where BAD = 65*, E lies on DC such that BED = 125*. A Find (i) ADE, (ii) CE. D 65 125 E B C
The figure shows a rectangle ABCD where the diagonals AC and BD intersect at E. D 52 C A Given that BC=52", find B (i) ADB, (ii) AD.
Find the values of the unknowns in each of the following rhombuses. (a) A 114 B (b) D- 38 C (c) D A 42 A B B
Find the values of the unknowns in each of the following squares. (a) D 82 C FB (b) D F C A B
Find the values of the unknowns in each of the following parallelograms. (a) D A 48 106" B (b) D 2df A B
Find the values of the unknowns in each of the following kites. (a) 100 (b) 40 B 61 C 26 C
Find the values of the unknowns in each of the following rectangles. (a) D a 54 C A (b) D 78 B C 39 E B
The figure shows a parallelogram ABCD where BAD=64. E lies on AB such that ADE=49. Calculate (i) ABC, (ii) CE. 64 49 E B
The figure shows a rectangle ABCD where the diagonals AC and BD intersect at E. E 63 Given that ACB=63", find (i) BEC, (ii) CE. B
The figure shows a rectangle ABCD. E lies on AB such that A hat DE = 51 deg and D hat CE = 68 deg . D 68 51" A Find (i) AD, (ii) CD. E B
The figure shows a rectangle ABCD. E lies on AB such that CD=85 and DE = 45*. Calculate (i) ADE, (ii) AD. 85" 45 B
In the figure, each side of AABC is produced. If AB AC, BD=BE and AF = DF, find ABC. D A C B E F

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