8.42 Chapter 8
In the figure, ABCD is a square. AOCE and BOD are straight
lines.
(a) Prove that BE = DE.
(b) If DE = DB, find +EBC.
(a) In 3BOE and 3DOE,
BO = DO
a AC = BD
` +BOE = +DOE = 90c
OE = OE
` 3BOE , 3DOE
` BE = DE
property of square
property of square
common side
SAS
corr. sides, , 3s
(b) DE = DB (given)
BE = DE (proved in (a))
` 3DBE is an equilateral triangle.
` +DBE = 60c (property of equil. 3)
+DBC = 45c (property of square)
` +EBC = +DBE - +DBC
= 60c - 45c
= 15c
Level 2
Example 17
D
A B
E
O
C
Solution
In the figure, ABCD is a rectangle and
AFEC is a straight line. It is given that
DF = AC and BE = AC.
(a) Prove that AF = CE.
(b) If EF = 3CE = 9 cm, find AC.
17
Instant Drill
➥ Ex 8C 17
Public Exam
Question 6
D
A B
F
E
C
PracticePractice
Class 8.3
1. In the figure, ABCD is a parallelogram. AOC, BOD and POQ are
straight lines. Prove that PO = QO.
A D
B C
P
O
Q
Short Question Tutor
ExamExam Get SetGet Set- 12.58
Chapter 12
Example 1
In the figure, two cars X and Y depart from point O at the same time. Car X
travels 16 km in the direction S48cW to point A while car Y travels 12 km
in the direction S42cE to point B.
(a) Find the compass bearing of B from A.
(Give the answer correct to the nearest degree.)
(b) A lorry travels from A to B in a straight line at a speed of 48 km/h.
Michelle claims that the lorry is closest to O after it travels for 12
minutes. Do you agree? Explain your answer.
(6 marks)
Solution
(a) With the notations in the figure,
i = 48c
In 3AOB,
+AOB = 48c + 42c
= 90c
` 3AOB is a right-angled triangle.
tan +OAB =
km
km
16
12
+OAB = 36.87c, cor. to the nearest 0.01c
i + +OAB = 48c + 36.87c
= 85c, cor. to the nearest degree
` The compass bearing of B from A is N85cE.
(b) In 3AOD,
cos +OAB = AO
AD
AD = AO cos +OAB
= 16 cos 36.87c km
Time required for the lorry to arrive D
= .cos
48
16 36 87c h
= 0.266 67 h, cor. to 5 sig. fig.
= 16.0 min, cor. to 3 sig. fig.
! 12 min
` The claim is disagreed.
N
N
O
A
B
48°
16 km 12 km
42°
N
N
O
A
B
48°
16 km 12 km
42°
i
D
1 for using the property of alternate angles to find the bearing
1 for using trigonometric ratio to find +OAB
1 for correct answer
1 for finding the length of AD
1 for finding the time required to travel from A to D
1 for correct conclusion with reasons
Expert
Tutor
Angles and Parallel Lines (I) T9.68i
In the figure, straight lines AB, CD and EF intersect at O. It
is given that +GOB = +BOD, +COE = 28c and OG = EF.
Find +AOF.
+DOF = +COE
= 28c
+GOB + +BOD + +DOF = +GOF
+BOD + +BOD + 28c = 90c
2+BOD = 62c
+BOD = 31c
+AOF + +DOF + +BOD = 180c
+AOF + 28c + 31c = 180c
+AOF = 121c
(P.9.11)
Level 2+
A
Example
Extra E 28°
C G
O
B
A
D
F
Solution ◀ vert. opp. +s
◀ adj. +s on st. line
Extra Examples Extra Example Worksheet 9
In the figure, DEF and BEG are straight lines.
(a) Find +CBG and +DEG.
(b) Hence, write down two pairs of parallel lines and
give reasons.
(a) x + 324c = 360c
x = 36c
+ABG + +ABC + +CBG = 360c
3x + 3x + +CBG = 360c
6x + +CBG = 360c
6 # 36c + +CBG = 360c
+CBG = 144c
+DEG + +DEB = 180c
+DEG + 144c = 180c
+DEG = 36c
(b) a +CBG = +DEB = 144c
` BC # DF (alt. +s equal)
a +DEG = +DFH = 36c
` BG # FH (corr. +s equal)
(P.9.22)
Level 2+
B
Example
Extra
3x x
324°
144°
3x
A
B
C
F
H
GD
E
Solution ◀ +s at a pt.
◀ +s at a pt.
◀ adj. +s on st. line
12
Book 3B Ch.8 • P.8.42 Book 3B Ch.12 • P.12.58
Book 1B Ch.9 • P.9.68i
拔尖 加辣
例題 DSE 題型
拔尖 加辣
拔尖 加辣
例題 程度2+
例題 考試題型