Form 1 MathematicsChapter 11

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

Missing HW Detention

SHW (II) 14th May (Tuesday)

OBQ 15th May (Wednesday)

CBQ 20th May (Monday)

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

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.

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 176 of Textbook 1B Class Practice

Pages 177 – 178 of Textbook 1B Questions 4 – 17

Pages 74 – 75 of Workbook 1B Questions 2 – 5

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

If AB = XY, BC = YZ and CA = ZX,

then △ABC △XYZ.

[Reference: SSS]

If AB = XY, B = Y and BC = YZ,

then △ABC △XYZ.

[Reference: SAS]

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:

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]

If C = Z = 90°, AB = XY and BC = YZ,

then △ABC △XYZ.

[Reference: RHS]

The table below summarizes all the conditions needed for two triangles to be congruent:

SSS SAS ASA AAS RHS

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

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.

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

= = .

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

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 191 of Textbook 1B Class Practice

Pages 191 – 192 of Textbook 1B Questions 1 – 10

Pages 80 – 83 of Workbook 1B Questions 1 – 6

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

If A = X, B = Y and C = Z,

then △ABC ~ △XYZ.

[Reference: AAA]

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).

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°

If = = ,

then △ABC ~ △XYZ.

[Reference: 3 sides proportional]

ax

by

cz

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

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

If = and a = x,

then △ABC ~ △XYZ.

[Reference: ratio of 2 sides, inc. ]

by

cz

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

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°

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 198 of Textbook 1B Class Practice

Pages 198 – 200 of Textbook 1B Questions 1 – 10

Pages 84 – 87 of Workbook 1B Questions 1 – 6

Missing HW Detention

SHW (II) 14th May (Tuesday)

OBQ 15th May (Wednesday)

CBQ 20th May (Monday)

Enjoy the world of Mathematics!

Ronald HUI