form 1 mathematics chapter 11. lesson requirement textbook 1b workbook 1b notebook before...
TRANSCRIPT
![Page 1: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/1.jpg)
Form 1 MathematicsChapter 11
![Page 2: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/2.jpg)
Lesson requirement Textbook 1B Workbook 1B Notebook
Before lessons start Desks in good order! No rubbish around! No toilets!
Keep your folder at home Prepare for Final Exam
![Page 3: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/3.jpg)
Missing HW Detention
SHW (II) 14th May (Tuesday)
OBQ 15th May (Wednesday)
CBQ 20th May (Monday)
![Page 4: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/4.jpg)
Congruent figures (全等圖形 )
1. Figures having the same shape and size are called
congruent figures.
e.g. Figures X and Y below are congruent figures.
2. Two congruent figures can fit exactly on each other.
X Y
![Page 5: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/5.jpg)
1. When a figure is translated, rotated or reflected,the
image produced is congruent to the original figure.
2. When a figure is reduced or enlarged, the image
produced will not be congruent to the original one.
![Page 6: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/6.jpg)
Symbol “ ” means “is congruent to”When two triangles are congruent,
(i) their corresponding sides (對應邊 ) are equal,
(ii) their corresponding angles (對應角 ) are equal.
e.g. If △ABC △XYZ, then
AB = XY,
BC = YZ,
CA = ZX,
A = X,
B = Y,
C = Z.
A
B C
X
Y Z
![Page 7: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/7.jpg)
Page 176 of Textbook 1B Class Practice
Pages 177 – 178 of Textbook 1B Questions 4 – 17
Pages 74 – 75 of Workbook 1B Questions 2 – 5
![Page 8: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/8.jpg)
There are four common conditions:
SSS: 3 Sides Equal
SAS: 2 Sides and Their Included Angle Equal
ASA : 2 Angles and 1 Side Equal(AAS)
RHS: 1 Right-angle, 1 Hypotenuses (斜邊 )
and 1 Side Equal
![Page 9: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/9.jpg)
If AB = XY, BC = YZ and CA = ZX,
then △ABC △XYZ.
[Reference: SSS]
![Page 10: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/10.jpg)
If AB = XY, B = Y and BC = YZ,
then △ABC △XYZ.
[Reference: SAS]
![Page 11: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/11.jpg)
Note: Must be SAS, not SSA!The abbreviation for this condition for congruent triangles is SAS, where the ‘A’ is written between the two ‘S’s to indicate an included angle. If we write SSA, then it means ‘two sides and a non-included angle’, but this is not a condition for congruent triangles. For example:
![Page 12: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/12.jpg)
If A = X , AB = XY
and B = Y,
then △ABC △XYZ.
[Reference: ASA]
or
If A = X , B = Y
and BC = YZ,
then △ABC △XYZ.
[Reference: AAS]
![Page 13: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/13.jpg)
If C = Z = 90°, AB = XY and BC = YZ,
then △ABC △XYZ.
[Reference: RHS]
![Page 14: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/14.jpg)
The table below summarizes all the conditions needed for two triangles to be congruent:
SSS SAS ASA AAS RHS
![Page 15: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/15.jpg)
Page 185 of Textbook 1B Class Practice
Pages 186 – 187 of Textbook 1B Questions 1 – 17
Pages 76 – 79 of Workbook 1B Questions 1 – 5
![Page 16: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/16.jpg)
Similar figures (相似圖形 )1. Figures having the same shape are called similar figures.
e.g. Figures A and B are similar figures.
2. When a figure is enlarged or reduced, the new figure is
similar to the original one. Note: Two congruent
figures always have
the same shape, and
so they must be
similar figures.
![Page 17: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/17.jpg)
Symbol “ ~ ” means “is similar to”When two triangles are similar,
(i) their corresponding angles are equal,
(ii) their corresponding sides are proportional.
e.g. If △ABC ~ △XYZ, then
A = X,
B = Y,
C = Z,
A
B C
X
Y ZXYAB
YZBC
ZXCA
= = .
![Page 18: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/18.jpg)
Example 1:In the figure, △ABC ~ △PQR.
Find the unknowns.
Since △ABC ~ △PQR,we have A = Pi.e. x = 44°
ABPQ
BCQR
=As
y40
2835
=
28 4035
y = = 32
ACPR
BCQR
=As
40z
2835
=
40 3528
= z
∴ z = 50
![Page 19: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/19.jpg)
Example 2:4
102y
=In the figure, △ABC ~ △ADE.
Find the unknowns.
Since △ABC ~ △ADE,we have ACB = AEDi.e. x = 104°
ADAB
DEBC
=As
2 104
y = = 5
410
33 + z
=
ADAB
AEAC
=As
3 1043 + z =
3 + z = 7.5
z = 4.5
![Page 20: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/20.jpg)
Page 191 of Textbook 1B Class Practice
Pages 191 – 192 of Textbook 1B Questions 1 – 10
Pages 80 – 83 of Workbook 1B Questions 1 – 6
![Page 21: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/21.jpg)
There are three common conditions:
AAA: 3 Angles Equal
3 sides prop.: 3 Sides Proportional
Ratio of 2 sides,: 2 Sides Proportional andinc. their Included Angle Equal
![Page 22: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/22.jpg)
If A = X, B = Y and C = Z,
then △ABC ~ △XYZ.
[Reference: AAA]
![Page 23: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/23.jpg)
Example 1:
Are the two triangles in the figure similar? Give reasons.
It is obvious that all corresponding angles are the same.
Yes, △ABC ~ △LMN (AAA).
![Page 24: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/24.jpg)
Example 2:In the figure, ADB and AEC are straight lines.
(a) Find ABC and ADE.
(b) Write down a pair of similar
triangles and give reasons.
(a) In △ABC and △ADE,
ABC
ADE
(b) △ABC ~ △AED (AAA)
= 180° – 60° – 80°
= 40°
= 180° – 60° – 40°
= 80°
![Page 25: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/25.jpg)
If = = ,
then △ABC ~ △XYZ.
[Reference: 3 sides proportional]
ax
by
cz
![Page 26: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/26.jpg)
Example 1:
Are the two triangles in the figure similar? Give reasons.
It is noted that
Yes, △LMN ~ △PQR (3 sides proportional).
34
12,3
3
9,3
2
6
PR
LN
QR
MN
PQ
LM
![Page 27: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/27.jpg)
Example 2:
Referring to the figure, write down a pair of similar triangles
and give reasons.
It is noted that
△ABC ~ △ACD (3 sides proportional)
5.14
6,5.1
5
5.7,5.1
6
9
DA
CA
CD
BC
AC
AB
![Page 28: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/28.jpg)
If = and a = x,
then △ABC ~ △XYZ.
[Reference: ratio of 2 sides, inc. ]
by
cz
![Page 29: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/29.jpg)
Example 1:Are the two triangles in the figure similar? Give reasons.
It is noted that
Yes, △XYZ ~ △FED (ratio of 2 sides, inc.).
FEDXYZED
YZ
FE
XY ,2
5.4
9,2
2
4
![Page 30: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/30.jpg)
Example 2:
(a) DCE
(b) △ABC ~ △EDC (ratio of 2 sides, inc.) (Why?)
In the figure, ACE and BCD are straight lines.
(a) Find DCE.
(b) Write down a pair of similar
triangles and give reasons.
= ACB (Why?)
= 54°
![Page 31: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/31.jpg)
To conclude what we have learnt in this section, we can summarize the following conditions for two triangles to be similar.
ad
be
cf
= =pr
qs
= , x = y
AAA 3 sides proportional ratio of 2 sides, inc.
![Page 32: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/32.jpg)
Page 198 of Textbook 1B Class Practice
Pages 198 – 200 of Textbook 1B Questions 1 – 10
Pages 84 – 87 of Workbook 1B Questions 1 – 6
![Page 33: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/33.jpg)
Missing HW Detention
SHW (II) 14th May (Tuesday)
OBQ 15th May (Wednesday)
CBQ 20th May (Monday)
![Page 34: Form 1 Mathematics Chapter 11. Lesson requirement Textbook 1B Workbook 1B Notebook Before lessons start Desks in good order! No rubbish](https://reader034.vdocuments.site/reader034/viewer/2022052312/56649f525503460f94c765dd/html5/thumbnails/34.jpg)
Enjoy the world of Mathematics!
Ronald HUI