1967-04-11 — Page 20

***

its history, geography, legends, anecdotes, and the rest n. The Hong Kong Yau Ma Ti Ferry Co. Ltd. (introduce) inta

operation a temporary vehicular ferry service,

(24)

Answers to the previous exercises

哦對送行退体事亚东在线及認悫是世界上

奧四第張五鱨

君二初三月年未丁度夏

WAH KIU YAT PO

雙 A

期鎏

日一十月四年七六九一鹰公年六十五國民中

育教僑華

中文中學會考試題預習專欄

** $

英文科

二三四)

鍾英·

Exercide '24

英文中

會考試題預習專欄上

1.

九七年

數學科

H

·歐陽謚文·

VATHEMATICS (24)

LESSUN 24: ARKAS

IMPORTANT THEOREMS.

A) Area theorems on triangles)

1) a =÷(base x height

2) Heron's Formula: Asia - à}{9 - b){• - a); om

(a+b+c)

31s on the game base (or equal bases) and between the same

parallels are equal in area.

B) Area theorems on quadrilateral:

1) Area of rect.= length x breadth.

2) Area of square sq. on one side.

3) Area of //gran m base x height

L) //gram (inc. rect,, sq., etc.) on the same base (or equal

bases) and between the same parallels are equal in area.

5) Area of trapezium = Average of two bases x height.

Median x height

6) Ares of rhombus — of the product of two diagonals.

*) Pythagoras theorem:

in art.4, the area of the square on the nypotenuse 18 equal to the sum of areas of the squares on the sides containing

the rt.L.

EXAMPLE 1: ABCD 18 » //gram; any line

parallel to BA cuts BC, AC, AD at

X, Y, Z respectively.

Prove that, A ARY=ADYZ.

PROOF: Jola DX.

Then, a DYZ + AGXY =1⁄2 of //gram ZKCD

= A CD

4. CXD, GAA are on the same både (CX) and between the same parallels ( CX//AD )

.. A CXD=ACKA Rance. DYZ + a CXY — A CID

}

=ACIA

=AXTA +ACK

ADIZ = AIYA,

EXAMPLE 2 AD is an altitude of ABC;P, are pulots on AD

produced such that DP AB and DAC.

Prove that: BQ=CP.

PROOF: 1 ABAC, then with the notation as ahowo

AMADEL BOC

A® ABD,802, PDC.CDA are ma

By Fythagoras,

From rta BQD:

From rtABDA:

**** BQ*-- BA*

From Ft 4 CPD:

From rt CDA:

BQ* = BD*+ DC*

BDBA - AD* — AÐ2+ DQ3

CP2= CD2+ UP* CD*= AC*- AD”

• CP2= AC2- AD2+ DP

*** OPAB and AG=DQ

CP* DQ- AD*+ AB*

BQ*

Hence, * -UP— 30.

given

in 0g.

NOTE: Similar proof will be applied to the case ABAC.

And, the proof is then completed.

EXAMPLE: K isthe mist of the diagonal BD or

lateral ABCD. Prove that the difference Between areas of A ABC and A ADC is emal to twice the areas ór ▲ AKO.

PROOF Let AC cuts BD at N.

(2) Suppose N lies between K & D as an own.

As KBA, KDA are on equal bases

(BXKD), and of the same altitude.

ABA AKDA

LAKHA- ▲ AND ≈ 4 KDA-A AND

AAKN

1.0. ANBA - A AND 2 AAKH

Similarly, ▲ NBC- & CND ≈≈ 2 A GKN

Adding AABC' – ACD÷2¬AÇK,

(11) IN lies between B & K

Then, ABC <AGD; hence ACD ABC= 2 — ARC..

Daneral Englisa

UOSTITUTO words or pùrases or similar MHAIRE TOR thosh underlined in the following sentences+

a. Go along. You're getting under my feeds

b. He went after three jobs last week-but without success.

When she ran up too many bills she could nearly alwave get round her father to settle them.

d. We tried to telephone you last night but the trunk line

was so busy that we couldn't get through.

e. They're turning out a great many new cars in Britain.

f. They live in the next stræet and cocasionally come round

to spend an evening with us.

g. That girl takes after her mother.

b. The air liner took off punctually.

1. They hadn't a room to spare so they put me up on the sofa,

j. In his will be set aside enough monar for the children's

education.

2. onange the following into Indirect Speech:

Fuck was sitting on the edze of a boat and looking very miserable.

"Hello, Huck!"

"Hello, Tom!"

Silence for a

minute

"Tom, if we'd left the tools at the

the money. Ob, aren't we unlucky!"

"It's not a dream, then!"

traa.

Dave ZOT

Dream! I've had horrible dreams all night, with that Spanish

devil chasing us all through them, cuse bin!"

"Don't ourae him. Find him? Track the money!"

"Tom, we'll never find him. And I'd be frightened to death if

I did see him,"

A. Combine each of the following groups Of sentences into ane

sentence:

a. We finished our breakfast,

Adele and I withdrew to the library.

Mr. Rochester had directed that the boracy sc010 Da used

es the schoolroom.

Most of the books were locked up debing glass doors.

There was one bookcase left open.

This bookcase contained erything that gould be needed in

the way of elementary Org

b. I took up the vessel with much difficulty i bosh bande.

In a most respectful pour drank to her ladykhin'a

health

I expregled the words 1 oud

This made the company laugh heartily."

Birlish.

was almost deafened by the noise of theirauch.

She master made me a sign.

I asked me to come to his trencher-side.

Liked on the table.

I was in great surprise all the

time.

I happened to stumble against a crust.

This made me fall flat on my face.

Luckily I received no hurt,

Use the verba in brackets in correct tenses:

Before the beginning of the 19th century, little (hear) of the island we now (call) Hong Kong.

h. Some people (say) the Dragon Boat Festival (start) by

men who (come) from what now (call) Indonesia.

c. Towards the end of the 13th century, the last of the

Sung Superore, (escape ) rom the Mongol invaders. (set)

up his capital in Kovli

A man (come)

bie Tace (seeD)

The sudden shock - against her father

enum gayJunkgen, and bigger until

) bor (stagger) and she (fall)

Mr. HV Morton (write) a good number of moạt interesting travel books, most of them, with a title (bezin) with "In Search of.

g. In this book we I taka) on & Tour of London and (tell) or

HONSKO

Consequently, the difference between the areas of As AZZ.

Aequal to 2 x AAMC.

EXAMPLE ↳ɛ (a) In ▲ ABC, AB5", B0=6a, /ABC=45". Calculata

the area of AABC and the length of ACA

(b) ABCD is a quadrilateral in which = [B=90°,

AB=6". BG10". A0=18" Prove that BD bisects ZADO

BOLUZION: (a) DERW AD&BG.

In A ABD

constr.

ADB=90′′ ZB=45 BAD=180-190+45)

fsum ofàâ

By Pythekoras.

Hence. area of a ABC =

BD=AD

2. AD

aldes opp. sáuals. AB***

(AD)(BC)

=

(2)(6) 10.6(89. in.

From rt.& ADC;

A

DC=80 - BD=6-2

By "Pythagoras, AC2=AD** DC*

-

18.57

AC 18.57 4,32(in.)

(b) PROOF: /A={B=90° - AD//BC.

Take a pt. on AD such that XD=10 Then, XDBC, XBCD is a //gram. From rt. A'ABX: AB=6

AX18 - 10=8 By Pythagoras. BX AB+ 1x2

2=6*+ B*= 100

10.

...BX

Hence in/gram XBCD, BXBC-10(in.)

XBCD is a rhombus.A

In which. BD is a diagonal, 80 bisosts / ADC;

EXAMPLIS 51. As shown; ABCD 28 a parallelogram,

and PQ, RS are parallel to AD, AB. Prove that (a) SPA + SPQA SPD (b) APR + a ASQ = ▲ ABD

(c) APKR KSCQ = 24BKD

PROOF: (a) Join KD, PR.

Join KA-

Then, A SPD A KPD + KPS+ 4 KSD

By the theorem of As on the same base and between the same // are equal in

area.

AKPD AKFRA APR AKSDA KSQ

"A KPS" in" common adding, AKPD #KSD-KPS

ASPA+ASPQ =

Then, ASQ KSA+@RSQ+AQEA

▲ KSA =•KSP=2 of //gram ESBP

KSQ = of //gram KSCQ

AQKA —A QKR ➡ of //gram QDRK *ASQ+APR of (KSBP+KSCQ+QDRK+APKB)

of ABCD A4B0

AAPS

va a sem úpon pegand APSKAKSQL KPS

SPD

5

C

@CK

最須痛的毒情也许你已有同感

互火車站的朋友送行,似乎很容易的事情,但我們 有些人從來沒有機會一定身手作長亭運到的表演。 紙在朋友中有人作長時間的逐行我們才会親到车站送行 朋友越親、润别越久,越早来运行,而且越难過.. 的程度通常時瀬和交情的厚成を比 其實在朋友的家中致大門外可举行隆室的送行 禮我們青时的面上私设话国足够表示彼此真切的 准过彼此都又再矜持但却不感觉尴尬,彼此的親密 Flute #FRANEN • ***PY VALAMELLI]. 12 Ap· 対地整えて私利 如果我依他的話不再就是行,他必定觉得我們很怪 而事要他當我想再定我們一面。我們亦響引使他孤颈 ...),我們伝時半、五兄到西時、馬具体願膃打呼

W

不

2. RAILKLIK HrjekJtÃsıb. Heik

凝视,好像不会说话的走就。武号害物话构,但又成 进应说话,心中总觉得运個朋友昨晚了经送剟而 他市管制我們表面とは同美術出る一層 隔膜。這樣尴尬的场面,彼此都不好受惟望乳笛

no one knew where TK A

mad some from nor who he was: "There were five willowa beside his house, thus he was generally

known as Mr. Five Willows. He was reticent, leading a quiet and leisure life. Honour and riches had never been attraction to bin. He was fond of reading but wasn't very particular to the meaning. Whenever he could make out what he was reading, bestras Bg overwhelmed with joy that he would forget bie méal. Ho redicted to drinking but owing to his poor. financial TERASA BIEen, he could hardly afford to buy wine very often. His

friends and relations fully aware of his difficulty, now axið Then invited him to drink at their houses. Whenever he was invited. he must drink until he' was drunk and when he got drunk..he took leave at once and had never stayed behind as an observation to courtesy. His bouge was empty within the surrounding walls almost without a single piece furniture anf it needed repairing so badly that it could hardly shelter Bid from the burning sun in summer and the biting wind in winter. Hay dressed in short shabby summer clothes all the year round and his food basket and wine gourd were repeated supty buts he didn't care. Be-asused himself in writing in which his interests were often expressed. Losa and gain in life mattered nothing to him. Be vas quite contented to and his lifə indthat kind of living.

JBRA

B

MNPQ is a rect

(0) Join KO

Then, BDG4BDK+a {CK+aCBK

or

ABDC= of //gram ABCD

DCK=4DQK +

of DQXR+ of 409K

A OBK =AGSK + Á SBK.

= of CSKQ +of SBPX

of ABCD=4BDK+ (DQKR+QCSK)

ABCI = 248DE+DQKA 2 or QCSK+ SBPX ABGL BQK +QCSK+ BBPX)+APKR APKR 2BD+QCSK APKROSK ABDK

HINTS & AMs. To Ex. 23

Proof

Proof. Join AB

ZYB=-208 ¢ «XYB»«XAÐ <Z Y X = 42 CB + LXAB

·AC, AD are diameters 2. ZABIOLABO WY

LABP + LABC » A the

CBD it a st. line

·±(<ACR+ ZBAC} (180 ABC } -90-1

jeto

of the miner ares AB, CD; and if M is the incentre of A ABC. Then,

EB=EM

Similarly, EA-EN But EB-EA. - EM=EN *A Emn is isos, JOMEG

$ is the M.p. of Co « CEGO - DE G

C

18. EG bisects the next, a of isos.AEMN.

EG IMME

Similarly. EGLPQ

But

B

1. MNOPQ a #gram

MNPA i £. F. G H as M.P.

Ploof: Show that

8) Proof: Jom PQ A&

PRC =

- 8+ Ex

(AADPE 4BPH (ARN)

(i)

<<=p, then DK=KP

*= then EPIKA tink is then the mid-point

of AD.

**PCA+LÆBE

=PCA +«CA& - CHK

2. H. R. Q, Pane con cyclic

text

= int opp. -

of a

ghad

EXERCISE 34

Proof Use

‚¢‚d to repléséné tée 43 as shown. cmb * deb

But, c+d+ «CAD=130

ABH 4m samTE

Segment

= Comp. of <BAE (HORBEY

LACF

- LACK

·AGR'

segment

AG birch « HGK.

Repeat the steps for BH & CR (they meet at of

6, Proof, Let EG be the

Draw OMLAB. ONICD Join OG

From & DOGM, OGN:

+AB=CD-LOM=ON

1. OGM-A DGN ERHA

2. MGENG

** ND - proved I

! Find the area of a

triangle

whose sides dre

modes Give reasons.

رو

2bp, (p** q2)

In a ABC. #B=8cm, AL - 9cm., and D. IS

A

point on BC

such that BD=Bd of the area of a ABC is 22h sy. cm.. find the distances of D' from AB and from ộc.

APQR

is a rectangle in which apg" BR=H! are points on QR. DP NÉP. such that RB = 3" QC = 8".

A

Calculate

B. C

las the area of

ABC

the length of the line joining the

of BA and

Q is any-pt.

diagonal Ac

that

•AURD=PQYe

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