Angles and Parallel Lines (I) 9.19
B Conditions for Parallel Lines
At primary level, we learnt how to draw parallel lines:
Step 1
First fix the ruler, then slide the
set square downwards along the
ruler to draw straight lines.
Step 2
AB and CD are a pair of parallel
lines.E
B
D
F
C
A a
b
In the above construction steps, we can see that a and b are a pair of
corresponding angles, and their sizes are both equal to the red angle
marked on the set square, i.e. a = b. In fact, we use the following
condition for parallel lines to draw parallel lines.
Condition 1 (corresponding angles)
If the corresponding angles formed by two
lines and a transversal are equal, then the
two lines are parallel.
i.e. In the figure,
if a = b, then AB # CD.
[Reference: corr. +s equal]
A
a
b
C
B
D
a and b lie on the same side of
the transversal EF, and on the
same side of AB and CD.
◀
In the figure, EH intersects AB and CD at F and G
respectively. Give reasons for AB # CD.
a +BFH = +DGH = 75c
` AB # CD (corr. +s equal)
75°
75°
E
H
G
F
A
C
B
D
Level 1
Example 7
Solution
In the figure, XY intersects AC and DF at B and
E respectively. Give reasons for AC # DF.
a +ABX = = 90c
` AC # DF ( )
7
Instant Drill
➥ Ex 9B 1
A C
D F
Y
X
B
E
© 牛津大學出版社 2020 鞏固練習 1A 冊 第 3 章
3.7
牛津數學新世代 1A
3 基礎代數 (一)
鞏固練習 3D
程度一
解下列各方程。[第 1−22 題]
1. 3(a 2) = a 2. 5(4 + b) = 9b
3. 6(3x 5) = 13x 4. 2(2y + 9) = 5y
5. 4(h + 1) = 14 h 6. k + 6 = 3(2k 3)
7. 4(h + 3) h = 0 8. 6(m + 7) + 5m = 9
9. 7(2s + 5) + 4s = 1 10. 5(3t 1) 3 = 7t
11. 8a 3(a + 6) = 27 12. 5m 2(9 4m) = 8
13. 22 + 3(u + 2) = 10u 14. 4 6(3t 1) = 7t
15.
5
8
a
= a 16.
3
7
b
= 2b
17.
35
yy
= 4 18.
82
xx
= 9
19. 6
7
k
= 7
3k 20.
4
3
c
c
21. 4
n = 3
8
5
n
22.
4
3p
=
6
5
2
p
程度二
解下列各方程。[第 23−42 題]
23. 5(m 3) = 2(4m + 9) 24. 3(5n 2) = 4(n + 4)
25. 9 4(1 p) = 3(8p + 5) 26. 3(n 6) + 39 = −2(7 + 2n)
27. 4(2k 1) + 5(5k 3) = 3 28. 8(2 r) 3(2r + 5) = −20
姓名:__________________________ 班別:__________( )
© 牛津大學出版社 2020 1A 冊 TSA 操練工作紙 2-1
TSA 操練工作紙 2
2 有向數
(a) 加法和減法
(i) x + (+a) = x + a (ii) x (a) = x + a
(iii) x + (a) = x a (iv) x (+a) = x a
(b) 乘法
(i) (+a) (+b) = +(a b) (ii) (a) (b) = +(a b)
(iii) (+a) (b) = (a b) (iv) (a) (+b) = (a b)
(c) 除法
(i)
b
a
b
a)(
)(
(ii)
b
a
b
a
)(
)(
(iii)
b
a
b
a)(
)(
(iv)
b
a
b
a
)(
)(
甲部:選出每題最佳的答案。
1. 計算 - 10 + 2(-5)。
A. -20
B. -13
C. 0
D. 40
2. 計算 4 - 4(-3)。
A. -3
B. 0
C. 3
D. 16
TSA 報告評論
很多學生能掌握有向數
的基本運算。
NA02-3
編號 重點
NA02-1 展示對整數在數線上的序
的認識
NA02-2 運用正數、負數和零去描述
諸如盈利與虧損、相對於地
面的樓宇層數等情況
NA02-3 進行有向數四則混合運算
(每一數式中作不超過 3
次運算)
NA04-4 在數線上表示有理數和無
理數*
* 在本章,題目只涉及有理數。
NA02-3
Angles and Parallel Lines (I) - Alternative Teaching Approach
3
B Angles Properties Related to Parallel Lines
In this section, we will study the properties of the angles formed by
parallel lines and a transversal (i.e. corresponding angles, alternate angles
and interior angles on the same side).
I. Corresponding Angles on Parallel Lines
Step 1
Draw two parallel lines
PQ and RS on a ruled
paper sheet. Then draw
a transversal XY to form
corresponding angles a
and b.
a
P Q
R S
Y
X
b
Step 2
Cut out the angle a in
the figure (the pink part
shown below).
P Q
R S
Y
X
b
a
Step 3
Place angle a onto angle
b to see whether angles a
and b can fit exactly.
P Q
R S
Y
X
b
a
According to the result in Step 3, are a and b equal? Compare the result with your classmates.
Ans
ActivityActivity
Class 9.2 Class e-Activity
From Class Activity 9.2, we can see that:
Property 1 (corresponding angles)
The corresponding angles formed by parallel lines and a transversal
are equal.
i.e. In the figure,
if AB # CD, then a = b.
[Reference: corr. +s, AB # CD]
A
C
B
a
b
D
e.g. In the figure, AB # CD.
x = 50c A
C
B
x
D
50° 130°
corr. +s, AB # CD
◀
Angles and Parallel Lines (I) 9.25
C Angles Properties Related to Parallel Lines
In this section, we will study the properties of the angles formed by
parallel lines and a transversal (i.e. corresponding angles, alternate angles
and interior angles on the same side).
I. Corresponding Angles on Parallel Lines
Step 1
Draw two parallel lines
PQ and RS on a ruled
paper sheet. Then draw
a transversal XY to form
corresponding angles a
and b.
a
P Q
R S
Y
X
b
Step 2
Cut out the angle a in
the figure (the pink part
shown below).
P Q
R S
Y
X
b
a
Step 3
Place angle a onto angle
b to see whether angles a
and b can fit exactly.
P Q
R S
Y
X
b
a
According to the result in Step 3, are a and b equal? Compare the result with your classmates.
Ans
ActivityActivity
Class 9.3 Class e-Activity
From Class Activity 9.3, we can see that:
Property 1 (corresponding angles)
The corresponding angles formed by parallel lines and a transversal
are equal.
i.e. In the figure,
if AB # CD, then a = b.
[Reference: corr. +s, AB # CD]
A
C
B
a
b
D
e.g. In the figure, AB # CD.
x = 50c A
C
B
x
D
50° 130°
corr. +s, AB # CD
◀
© Oxford University Press 2020 8.9 Consolidation Exercise 1B Chapter 8
10. In each of the following figures, ABCD is a rectangle whose sides are either horizontal or
vertical.
(i) Find the coordinates of B and D.
(ii) Is ABCD a square? Explain your answer.
(a)
(b)
11. In the figure, PQRS is a trapezium.
(a) Find the coordinates of R.
(b) Given that QP = 13 units, find the perimeter of trapezium
PQRS.
12. Given that the distance between points M and N in the figure is
9 units, find the value of n.
13. Given that the distance between points P and Q in the figure is
12 units, find the value of q.
Level 2
14. For each of the following pair of points,
(i) determine whether the line passing through them is a horizontal line or vertical line,
(ii) find the distance between them.
(a) K(5.4 , 2.7), L(9.6 , 2.7)
(b)
3
2
6,
3
1
4P ,
3
1
2,
3
1
4Q
A(3 , 2)
A(4 , 8)
Q(5 , 5)
M(10 , 3) N(n , 3)
SECTION C: All working must be clearly shown.
Write the mathematical expressions, answers and statements/conclusions in the
spaces provided.
25. Find the area of the triangle in the figure.
Ans
26. Find the area of the trapezium in the figure.
Ans
MSS26-2
MSS26-2
Comment from TSA report
Some students need improvement on
calculating areas of simple figures. Also,
some students used a wrong unit (cm
2).
P
Q R(5, 1)
(2, 1)
(6, 7)
y
x
O2 1 1 2 3 4 5 6 7 8
8
7
6
5
4
3
2
1
1
2
H (6, 1)
A
B C
D
(4, 1)
y
x
O
5 4 3 2 1 1 2 3 4 5
5
4
3
2
1
1
2
3
4
5
(4, 3) (2, 3)
(5, 1)
With the notations in the figure,
coordinates of H = (6, 1)
QR = (5 - 2) units = 3 units
PH = (7 - 1) units = 6 units
Area of the triangle PQR
= × QR × PH
= × 3 × 6
= 9 sq. units
2
1
2
1
With the notations in the figure,
AD = [2 - (-4)] units = 6 units
BC = [5 - (-4)] units = 9 units
AB = (3 - 1) units = 2 units
Area of the trapezium ABCD
= × (AD + BC) × AB
= × (6 + 9) × 2
= 15 sq. units
2
1
2
1
14
Book 1B Chapter 9
C Conditions for Parallel Lines
At primary level, we learnt how to draw parallel lines:
Step 1
First fix the ruler, then slide the
set square downwards along the
ruler to draw straight lines.
Step 2
AB and CD are a pair of parallel
lines.E
B
D
F
C
A a
b
In the above construction steps, we can see that a and b are a pair of
corresponding angles, and their sizes are both equal to the red angle
marked on the set square, i.e. a = b. In fact, we use the following
condition for parallel lines to draw parallel lines.
Condition 1 (corresponding angles)
If the corresponding angles formed by two
lines and a transversal are equal, then the
two lines are parallel.
i.e. In the figure,
if a = b, then AB # CD.
[Reference: corr. +s equal]
A
a
b
C
B
D
a and b lie on the same side of
the transversal EF, and on the
same side of AB and CD.
◀
In the figure, EH intersects AB and CD at F and G
respectively. Give reasons for AB # CD.
a +BFH = +DGH = 75c
` AB # CD (corr. +s equal)
75°
75°
E
H
G
F
A
C
B
D
Level 1
Example 12
Solution
In the figure, XY intersects AC and DF at B and
E respectively. Give reasons for AC # DF.
a +ABX = = 90c
` AC # DF ( )
12
Instant Drill
➥ Ex 9C 1
A C
D F
Y
X
B
E
23
替補教學建議
Alternative Teaching
Approach
鞏固練習
Consolidation Exercise
TSA 操練工作紙
TSA Drilling Worksheet
學生課本以「先條件,後性質」介紹與平行線有
關的角
替補教學建議則以「先性質,後條件」介紹與
平行線有關的角
充足基礎訓練,順利銜接打穩根基
• 模擬TSA題目
• 對應基本能力指標
• 大量程度一及程度二題目
• 操練或家課之用
課後