F.1 Mathematics Supplementary Notes
Chapter 8 & 10
4/2002
Chapter 8 Introduction to Geometry
Chapter 10 Congruence and Similarity
Important Terms
Geometry
line segment
end point
point of intersection
acute angle
right angle
obtuse angle
congruent to
幾何學
線段
端點
交點
銳角
直角
鈍角
全等於
Name:___________(
isosceles triangle
equilateral triangle
polygon
regular polygon
parallel lines
perpendicular lines
diagonal
proportional
等腰三角形
等邊三角形
多邊形
正多邊形
平行線
垂直線
對角線
成比例
centre
circumference
diameter
radius
solid
cross-section
vertices
similar to
)Class: F.1 (
圓心
圓周
直徑
半徑
立體
橫切面
頂點
相似於
Exercise 1
1. Refer to the figure
A
D
C
B
(a) Produce(延長) BA and CD to meet at P.
(b) Produce BC to Q so that the length of CQ is less than that of BC.
(c) Join AQ to meet the line segment CD at M.
(d) Join the two diagonals AC and BD，and mark the point of intersection by F.
2. Refer to the figure
Angle
E
Kind
(a) ABF
(b) EBA
(c) FBC
(d) b
acute angle
___________
___________
___________
(e) ABC
(f) EBD
___________
___________
b
D
250
F
400
A
B
P. 1
C
)
F.1 Mathematics Supplementary Notes
3.
Chapter 8 & 10
4/2002
In the figure, AB＝BC＝CA＝CD.
A
(a) The isosceles triangles are
_________________________
and an equilateral triangle is
_________________________
(b) ACB＝__________________
D
E
d
70
0
b
B
C
(c ) b + d = __________________
4.
Find the unknown in each of the following triangles.
(a)
(b)
3x
29 0
x–5 0
x
a
27 0
(c)
(d)
48
b
41 0
17
x
*5. In the figure DCA=DCB , DBA=DBC , BAC=64, find x.
A
64
D
x
B
C
P. 2
F.1 Mathematics Supplementary Notes
Chapter 8 & 10
4/2002
P. 3
Exercise 2
1.
In each of the following pair of triangles, decide whether ABC is congruent to the other
For each pair of congruent triangles, give the abbreviated reference.
(a)
(b)
AB = FD
BC = DE
AC = FE
ABC  FDE (SSS)
(c)
(d)
(e)
(f)
triangle or not.
F.1 Mathematics Supplementary Notes
(g)
2.
Chapter 8 & 10
(h)
In each of the following, find out which two of the given triangles are congruent and
give the abbreviated reason.
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F.1 Mathematics Supplementary Notes
Chapter 8 & 10
4/2002
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F.1 Mathematics Supplementary Notes
Chapter 8 & 10
4/2002
Conditions for Similar Triangles
∠BAC=∠QPR
∠ABC=∠PQR
∠BCA=∠QRP
(equiangular)
( or AAA)
(3 sides prop.)
∠ACB=∠PRQ
(2 sides prop. inc.  eq.)
Exercise 3
1.
In each of the following, state whether the given pair of triangles are similar
or not. For each pair of similar triangles, give the abbreviated reference.
ABC RPQ (3 sides prop.)
Reasoning Steps
CB 5 1


QP 15 3
BA
4 1


PR 12 3
CA 3 1
 
QR 9 3
CB BA CA 1



QP PR QR 3
 ABC RPQ (3 sides prop.)
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F.1 Mathematics Supplementary Notes
1.
Chapter 8 & 10
4/2002
A
2.
A
Y
X
Z
Y
Z
C
B
C
3.
A
P
Q
Z
C
4.
R
B
B X
Q
A
B
C
P
R
P. 7
F.1 Mathematics Supplementary Notes
5.
Chapter 8 & 10
X
4/2002
6. A
C
Z
X
B
Y
C
A Z
Y
B
7.
8.
9.
10.
11.
12.
P. 8
F.1 Mathematics Supplementary Notes
Chapter 8 & 10
13.
14.
15.
16.
17. Given that ABC  XYZ, BAC = 1230, ABC = 250, AB = 6cm, XY = 2cm, YZ = 3.2cm,
find
(a) XYZ
(b) YZX
(c) BC.
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F.1 Mathematics Supplementary Notes
Chapter 8 & 10
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P. 10
18. Given that ABC  DEF, AB = 3cm, AC = 5cm, BC = 7cm, EF = 8.4cm, BAC = 1200,
find (a) FDE
(b) DE
(c) DF.
Level II
19. In each of the following, find out which two of the given triangles are similar and prove it.
20.
(a)
(b)
In each of the following, find out a pair of similar triangles and prove it, hence find the value(s) of
the marked unknowns.
F.1 Mathematics Supplementary Notes
(c )
(d)
(e)
Chapter 8 & 10
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Chapter 8 & 10
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F.1 Mathematics Supplementary Notes
Chapter 8 & 10
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F.1 Mathematics Supplementary Notes
Chapter 8 & 10
4/2002
P. 14