Assignment Unit 8 Geometry

8/8/2019 Assignment Unit 8 Geometry

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Sha Tin College Mathematics Department KS 4 ASSIGNMENT Geometry 1

Name:

Sha Tin College Mathematics DepartmentKey Stage 4 Extended Level Course

Unit 8 Assignment: Geometry Total

/67(76 for JXL/CI)

Angle Relationships

Need to Know Sketch the angle relationship here

Angles on a line add to 180o

Angles at a point add to360o

Vertically opposite angles are equal

Angles in a triangle add to 180o

Angles in an equilateral triangle are equal

ie. 60o

Base angles of isosceles triangles are equal

Corresponding angles in parallel lines are

equal

Alternate angles in parallel lines are equal

Co-interior angles in parallel lines add to

180o

Complementary angles add to 90o

Supplementary angles add to 180o

Sum of exterior angles of n sided

polygon is 360o

Exterior angle of regular nsided polygonis 360o/ n


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Sum of interior angles of n sided polygon

is (n-2) x 180o

Interior angle of regular n sided polygonis ((n-2)x 180o)/n

The angle in a semi-circle is 90o

The angle at the centre of a circle is double

the angle at the circumference.

Angles from the same arc are equal

Opposite angles in cyclic quadrilaterals aresupplementary.

The angle between a tangent and a radiusof a circle is 90o

Tangents from an external point are equalin length.

Conditions that need to exist for trianglesto be congruent i.e. SAS, AAS, SSS andRHS

If scale factor (SF) for length is k thenSF area = k2

SF volume = k3

A: Angle Relationships#1 non calc In the diagramABCis a straight line, angleEAB = 90, angleBCD = 51

and angle CDE= 125. B is parallel toDC.

NOT TO SCALE


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(a) Calculate(i) angleAED,

Answer (a)(i) angleAED = [1]

(ii) angleEBC.

Answer (a)(i) angleEBC= [1]

(b) What is the special name of quadrilateralEDCB?Answer (b) EDCB is a [1]

Total for Section A /3

B: Angles in Polygons

#1 non calc The hexagonABCDEFhas rotational symmetry of order 2 about O.

Angle FAB = 120, angleABC= 130 and angle CDE= 120.

(a) Write down angleDEF.Answer (a) AngleDEF= [1]

(b) Calculate angleBCD.

Answer (b) AngleBCD = [2]

NOT TO SCALE


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#2 Each exterior angle of a regular polygon is 24.Calculate the number of sides of the polygon.

Answer [2]

#3

Show by calculation, that an equilateral triangle, a regular polygon and

a regular 24 sided polygon fit together exactly at the point X, as shownin the diagram.

Answer

[5]

NOT TO SCALE


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#4

#9

The diagram represents part ofa regular octagon ABCD . . .

with diagonalACdrawn.

NOT TO SCALE

(a) Calculate angleABC.

Answer (a) AngleABC= [2]

(b) Calculate angleACD.

Answer (b) AngleACD = [2]

Total for Section B /14

C: Angles in Circles#1 The chordAB of a circle, centre O, is parallel to the radius OT. Angle TAB = 41.


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Calculate

(a) angle OTA,Answer (a) Angle OTA = [1]

(b) angle TOB.

Answer (b) Angle TOB = [1]

#2

Find

(a) BDO ,

Answer (a) BDO = [1]

(b) BDA ,

Answer (a) BDA = [1]

(c) OAD ,

Answer (a) OAD = [1]

(d) BCD .

Answer (a) BCD = [1]

AOB is a diameter of the circle,centre O.

BCand OD are parallel.

20CBD .

NOT TO SCALE


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#3 AB is the diameter of a semicircleACB.The linesAG, CFandBEare parallel.

EBC x and CAG y .

NOT TO SCALE

(a) Write down the value of ACB .Answer (a) ACB = [1]

(b) Write an expression for(i) BCF in terms ofx ,

Answer (b)(i) BCF = [1]

(ii) ACF in terms ofy .

Answer (b)(ii) ACF = [1]

(c) Use your results from parts (a) and (b) to prove that 90x y .Answer (c)

[1]

#4 The diagram represents a regular pentagonABCDEinscribed in a circle, centre O.

The tangents atA andB meet at W.

NOT TO SCALE


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Calculate

(a) angleBCD,[2]

(b)

angle CBD, [2]

(c) angle OAB, [1]

(d) angle WAB, [1]

(e) angleAWB. [2]

Total for Section C /18

D:Symmetry, Similarity#1 Two different quadrilaterals each have one, and only one, line of symmetry.

In quadrilateralA, the line of symmetry is a diagonal.In quadrilateralB, the line of symmetry is not a diagonal.

Draw each of the quadrilaterals, showing the line of symmetry, and write downtheir special names.

Answer

Name Name [4]

QUADRILATERAL A QUADRILATERAL B


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#2 Triangles P and Q are similar.

NOT TO SCALE

Their longest sides are 3 cm and 7 cm respectively.

(a) Write down the ratio of their perimeters.

Answer (a) Perimeter ofP : Perimeter ofQ = : [1]

(b) Calculate the ratio of their areas.

Answer (b) Area ofP : Area ofQ = : [1]

#3 The bowls shown in the diagram below are similar.

NOT TO SCALE

The capacity of the smaller bowl is 300 ml.

Calculate the capacity of the larger bowl.

Answer ml [2]


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#4 The diagram shows a street lightAE, which is 7 metres high.A girl, who is 1.7 metres tall, stands 5 metres away from the point E.

Her shadow isx metres long.

NOT TO SCALE

Explain why1.7

5 7

x

x

.

Answer [1]

#5 A,B and Care three similar containers.Their heights are 40 cm, 30 cm and 15 cm respectively.

Container Chas a surface area of 450 cm2 and has a capacity of 0.8 litres.

Calculate

(i) the surface area of containerA,

Answer (b)(i) cm2 [3]

(ii) the capacity of containerB.

Answer (b)(ii) litres [3]


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#6 O is the centre of the circle.

AngleBOD = 132.

The chordsAD andBCmeet at P.

(a) (i) Calculate anglesBAD andBCD. [2]

(ii) Explain why trianglesABP and CDP are similar. [1]

(iii) AP = 6 cm, PD = 8 cm, CP = 3 cm andAB = 17.5 cm.Calculate the lengths ofPB and CD. [4]

(iv) If the area of triangleABP is n cm2, write down, in terms ofn,the area of triangle CPD. [2]

(b) (i) The tangents atB andD meet at T.

Calculate angleBTD. [2]

(ii) Use OB = 9.5 cm to calculate the diameter of the circle

which passes through O,B, TandD, giving your answer

to the nearest centimetre. [3]

Total for Section D /30


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Check List for Unit 8 Geometry

CAN DO STATEMENTS Unit 8 Geometry

SyllabusReference Main Learning Objectives Tick here

4.1 RECAP (A) Know the meaning of these words with respect to

Geometry. Acute, obtuse, right angle, reflex, parallel,perpendicular, equilateral, isosceles, regular, pentagon, hexagon,

octagon, rectangle, square, kite, parallelogram, trapezium,Congruent

NEW Know the meaning of these words with respect to Geometry.

Similar, rhombus.

4.3 RECAP (A) Be able to measure and draw angles in degrees.

4.4 RECAP Be able to calculate missing angles by knowing the following angle properties.Angles round a point add to 360o, angles on a straight line add to 180o, vertically opposite angles are

equal, alternate angles on parallel lines are equal, corresponding angles on parallel lines are equal, co-interior angles on parallel lines are supplementary, angles in a triangle add to 180o

4.4 RECAP Be able to calculate missing angles by knowing thefollowing angle properties. Angle sum of a triangle, quadrilateral

and polygons. Find interior and exterior angles of regular and

irregular polygons.

4.9 NEW Be able to calculate missing angles by knowing that;

the angle in a semi-circle is 90o, the angles at the centre of a circle

is double the angle at the circumference.

4.9 NEW Be able to calculate missing angles by knowing that; anglesfrom the same arc are equal and that opposite angles in cyclic

quadrilaterals are supplementary.

4.8 NEW Be able to calculate missing angles by knowing that the

angle between a tangent and a radius of a circle is 90o and tangents

from an external point are equal in length.

4.2 RECAP Be able to draw and describe the symmetry of a 2D and

3D shape. Including line and rotational symmetry.

4.6 NEW Understand the meaning of mathematical similarity. Use the

relationships between the areas and volumes of similar shapes to be

able to find missing dimensions.

4.6 NEW Find area and volume of similar figures using scale factor for

area and volume.

4.6NEW

Use the relationships between volumes and surface areas ofsimilar solids.

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Assignment Unit 8 Geometry