Key Stage 3
Measures, Shape & Space Dimension
Learning Unit : Angles related with Lines and Rectilinear Figures
Learning Objectives：
· recognize different types of angles
· explore and use the angle properties associated with intersecting
lines and parallel lines
Programme Title : Angles and Lines
Programme Objectives
1. Recognize the angles (vertically opposite angles and adjacent
supplementary angles) associated with intersecting lines and their
properties.
2. Recognize adjacent complementary angles and its application in using a
clinometer.
3. Recognize the angles (corresponding angles, alternate angles, interior
opposite angles) associated with parallel lines and a transversal; and their
properties.
4. Apply the knowledge of angles associated with parallel lines and a
transversal in interesting mathematical problems and real-life situations.
Programme Outline
A group of students of the mathematics club uses a clinometer to measure the
height of their school building. In the activity, the students recognize that the
angle of elevation of an object obtained by the clinometer is related to the angle
between its plumb line and the vertical. In explaining the principle by their
teacher, they review the properties of vertically opposite angles, adjacent
supplementary angles and adjacent complementary angles.
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An interesting quiz about angles associated with parallel lines is displayed on
the mathematics notice board. The teacher guides the students to explore the
properties of corresponding angles, alternate angles and interior opposite angles
in order to solve the problem.
Finally, the converse property (if the corresponding angles of two lines and a
transversal are equal, then the two lines are parallel) is elaborated through the
context of playing pool.
Worksheet Answers
1. corresponding angles， BE CD
alternate angles， AC FD
adjacent supplementary angles
2.
xy90
3.
B130
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Key Stage 3 ETV Programme《Angles and Lines》
Worksheet
1. Write down the reasons for the respective steps in the following solution：
A
B
C
In the diagram, AC FD, BE CD,
30
D=70, ABF=30,
x
find the value of x.
BE CD，
BEF=D=70 (
70
) F
AC FD，
CBE=BEF=70 (
E
D
)
CBE x30=180 (
x=80
)
E
2. In the diagram, AB CD,
FI, GI are the angle bisectors of AFG and
CGF respectively.
(a) Find the value of x  y;
(b) hence, prove that I is a right angle.
C
A
F
B
x
I
yo G
D
H
3. In the diagram, BA DE,
D=140, C=90,
find B.
A
B
E
140o
C
D
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