Download Core unit 8 Geometry

Name:
Sha Tin College Mathematics Department
Key Stage 4 CORE Level Course
Unit 8 Assignment: Geometry
Need to Know
Angles on a line add to 180o
Total
/55
Angle Relationships
Sketch the angle relationship here
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 “n”sided polygon
is 360o / n
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry
1
Sum of interior angles of “n” sided polygon
is (n-2) x 180o
Interior angle of regular “n” sided polygon
is ((n-2)x 180o)/n
The angle in a semi-circle is 90o
The angle between a tangent and a radius
of a circle is 90o
Tangents from an external point are equal
in length.
A: Angle Relationships
#1
NOT TO SCALE
Two of the three line segments in the letter
(a)
Calculate the value of
(i)
(ii)
(b)
N shown in the diagram are parallel.
p,
Answer (a)(i) p =
[1]
Answer (a)(ii) q =
[1]
q.
Mark the centre of rotational symmetry on the diagram, and label it O. [1]
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry
2
#2
NOT TO
SCALE
In the diagram WXYZ is a parallelogram.
V is a point on XY. Angle WVZ = 90.
Calculate the values of a, b and c.
Answer a =
b=
c=
[4]
#3
NOT TO SCALE
The diagram represents a church window, which consists of a rectangle
surmounted by a semi-circle. The line through B and F is the line of
symmetry, and BD is parallel to FG.
Angle BAD  90 and angle ADB  30 .
Calculate each of the following angles:
ABD =
DBF =
BFG =
BFH =
GFH =
[5]
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry
3
#4
In the diagram, EAB is parallel to DC.
AE = AD, angle ABC  110 and angle EAD  52 .
NOT TO
SCALE
(a)
(b)
What is the geometrical name of the quadrilateral ABCD?
Answer (a)
[1]
Answer (b)(i) x =
[1]
Answer (b)(ii) y =
[1]
Answer (b)(iii) z =
[1]
Calculate the value of
(i)
(ii)
(iii)
x,
y,
z.
Total for Section A
/16
B: Angles in Polygons
#1
A decagon is a polygon with ten sides.
Calculate the interior angle of a regular decagon.
Answer (a)
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry
[3]
4
#2
The diagram shows the top of a table used for committee meetings.
NOT TO SCALE
XY is a line of symmetry, and BJIE is a straight line.
CD is parallel to JI and to AL. BC is parallel to KJ.
AB is parallel to LK. Angle BAL = 90, and angle CBJ = 30.
(a)
Calculate the size of each of the following interior angles
marked in the polygon ABCDEFGHIJKL.
Answer (a)
[4]
DEF =
BCD =
LKJ =
KJI =
(b)
(i)
Write down the size of each of the twelve interior
angles of the polygon. Then find their sum.
Answer (b)(i)
Sum =
(i)
Find the value of the expression 180(n  2) , when n = 12.
Answer (b)(ii)
(ii)
[2]
[1]
Comment on your answers to (b)(i) and (b)(ii).
Answer (b)(ii)
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry
[1]
5
#3 What is the size of an exterior angle of a regular nonagon?
Answer ___________________ [2]
Total for Section B
/13
C: Angles in Circles
#1
AD is a tangent to a circle,
centre O.
NOT TO
SCALE
BOC is a diameter.
Given that angle ADB  35 ,
calculate
(a)
(b)
angle BDO,
Answer (a)
[1]
Answer (b)
[1]
angle ODC.
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry
6
#2
NOT TO
SCALE
RST is a tangent to circle, centre O.
PS is a diameter.
Q is a point on the circumference
and PQT is a straight line.
Angle QST = 37.
Write down the values of a, b, c and d.
Answer a =
b=
c=
d=
[4]
#3
AOC and BOD are diameters of the circle, centre O.
(a)
If angle BDC  35 , calculate angle CAD.
Answer (a) Angle CAD =
(b)
Draw the line of symmetry of the diagram.
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry
[2]
[1]
7
#4
NOT TO SCALE
In the diagram ADE is a tangent to the circle, centre O.
ABOC is a straight line, angle BAD  30 and AB = BD.
Calculate
(a)
(b)
angle CDE,
Answer (a) Angle CDE =
[2]
Answer (b) Angle BCD =
[2]
angle BCD.
Total for Section C
/13
D:Symmetry, Similarity
#1
(b)
Eight of the interior angles of this star are right angles.
What is the size of each of the eight interior (reflex) angles?
Answer (b)
(c)
Draw the lines of symmetry on the star at the TOP of the page.
(d)
Write down the order of rotational symmetry of the star.
Answer (d)
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry
[3]
[2]
[1]
8
#2
The diagram shows a design made of four overlapping circles, each of
radius 10 cm. Each centre is shown on the diagram.
(a)
On the diagram, draw the lines of symmetry of the design.
(b)
Give the order of rotational symmetry of the design.
Answer (b)
2cm
[2]
[1]
x
#3 Triangles P and Q are similar. Calculate the length of side x.
Answer ___________________ [2]
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry
9
#4
The bowls are similar. The diameter of the large bowl is 14cm, calculate the diameter of
the small bowl.
Answer ___________________ [2]
Total for Section D
/13
Check List for Unit 8 Geometry
CAN DO STATEMENTS Unit 8 Geometry
Main Learning Objectives
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.
RECAP (A) Be able to measure and draw angles in degrees.
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.
RECAP Be able to calculate missing angles by knowing the following angle
properties.
Alternate angles on parallel lines are equal, corresponding angles on parallel lines
are equal, co-interior angles on parallel lines are supplementary.
RECAP Be able to calculate missing angles by knowing the following angle
properties.
Angles in a triangle add to 180o , base angles of isosceles triangles are equal.
Tick
RECAP Be able to calculate missing angles by knowing the following angle
properties. Angle properties of a quadrilateral.
RECAP Be able to calculate missing angles by knowing the following angle
properties. Angle sum polygons. Find interior and exterior angles of regular and
irregular polygons.
NEW Be able to calculate missing angles by knowing that;
the angle in a semi-circle is 90o
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry
10