辦四張乪第
日五初月三年申虎麼靈
WAH KIU YAT PO #
A
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1968
英文中
數學科
(=)
歐陽鎰文
LESSON 2 3
MAJKEMATICS (23)
AREAS
Important the prems
Acta hensNS DA A
Pranac basera height 3-
2, Heron's farmaca
Area == 's{s-α){ $b){5-07.
5= f(0+b+c)
$, As on ke some base to equal bases) and between
the
an equal in
same parallels
B, Brea theorems on quadrilateral
1. Area of rect =
length x breadtik
2. Area of square spon
2, Ama o igram =
[4, #gram (nine
one side.
basc x height.
ano
ARCH #1 on the same bas (n equal
bases) and between the same parallels are equal in
CLARO
15, Area of trapezium =
<; Ama” of rhombus
Slythegons thenɩm,
Average of two bases x height
= median x
height
t of the product of two diagonals
In a A, the area of the square on the hypotenust aquals the sum of areas of the squares on ture
CHAR_1yAD*is an altitude of a ABC; P. Q are points
on Ab produced such that DP¬AB DQ=AC, Prove that BQ=CP.
TRODE = If AB > AC, then, from the fig, as shown.
ADP L BDC
**A, ABD, BDQ.PDC, CDA are 14.4,
By Pythagoras' theorem
From HaS@D» -8Q*= 8p*+ ba*
From #fa &ÞA› BD*= BA” – AD*
`r, 8Q*= BA*– AD2+ DQ*.. From via C7 11° ©P*% ¢q'+DP* From dacBAI CPU AÇ ̃— AÐa
Əvom (1) ► <*), '% DP=AB ← AĊ = PQ
`{CP*= »a ̃ – A y2 + AB*
* BRID CP-BQ.
AC
*
= 61-60√
218.37
18·57
A
.*. AD/BC
Take a popiat 2 on AD 6.4 XD=1,
XD AC
. X8CD is ham AABX +
By Tythagoras,
a Ngram (oga site 66)
AB=6 AX=18=10 m 2
6x*■ A8** A**
* B* fo
8
= foo
Hence, in #gram XBCD: 8x=80 = 10 (in 2
X BCD is a rhombus; BD is a drag. AD bisechs ADC
D
EXAMPLE 4:
As shown. ABCD A
a para regiam and Pa, RS are parallel to AD, AB. Prove that ca) & SPA + a SPQ=<$PD (b) 4 APR+ — ASQ = ABD <<) APKR - KSCQ=2. 48kD A
(a) Join KD, PR
PPOF
D
Then ASPD = <KPD+ «<P3 **
· As on the same base ona between the same lis are squat in areu ;
s KPD = OKPR = & APR = <AP$ AKS DI AKSO
A KPS in Common
Adding, ARPD+ «KSD+ «KFS = APS + KSQFORPS
ASPATA S P Q = 4 SPD
*
[(b) Join KA
Then, * ASG = AKSAT AKSA PARKA
= Axs! =
Hyam KSBP
GAN * AQKA EI 4 Ağum ADRK
APA = 248 ( KSBP + KSE
* of ABCD, MAADD.
Jom KC
Then ̧ a&DC = ABDK + ABCR + ACER,
* BDC=± of #gram ABCD
4 DC k = ADAK TAQCK
➡★ of #grams (PQKR+&CSK)
... COK» ACSK+ 458K
=£ of {cska + SBPK)
A
>
A
(8 + ÁPKR)
#
». ‡ of ABCD = ABPR + ŽE PAKK+Q¢sk} + {(C3KQ+ SBPK.
A8CD= 2·4BDK + DQKR+2·QCSK + 58FK
ABCom (DRKRTÜLŞAL SBPKY+ APKK
4. APKR 1. 2. a SPA + OCSA
APKR -
杯
日二月四年八六九一零公年七十五國民中
育教導
1968
英文中學문
英文科(廿三)
•
MRS - BENNETT •
English (23)`
Answers to Paper 22
1. The writer said that navigation in thick,
mountainous jungle is difficult because one je
unable to find one's position on the map; one can
see only up to 100 yards and, even if visible, all the mountains look alike anyway, also it is impossible to estimate the distance one has travelled from the amount of effort that one has used. Above all one is unable to proceed in the chosen direction because of the difficult terrain. sven following a ridge, unless very sheer and clearly marked, is useless for one can easily choose the wrong one.
are
190 words. The words "The writer said that
never included_in_the_total number of words in a summary)
The average N... 19 more intelligent than the private soldier and for this reason might last longer in the jungle.
3. The writer tells us that leeches cling with their teeth to the bodies of humans submerged in wateri that there is a belief that leeches should not be pulled off but removed by touching them with salt. tobacco, a solution of areca nut, or a cigarette-, end: that, however the leeches are removed, the wounds they have caused bleed and become poisoned.) (Be careful in this type of question not to add
whything which is not in the passage. The questio was what does the writer tell us about leeches?" not "what do you know about leeches?".)
ine writer means that, previously, he had thought of himself as being good at map reading..
3.nameless Larrors - fears which are unknown and
therefore cannot be name
creen hall - the writer is suggesting that the
jungle, which is predominantly green, is like hell; that 19, the most unpleasant place imaginable.
sehool of thought people who have the same
on a particular topic - in this case their altitude to the jungle.
vier
smeil landslide has opened up a window - the writer is comparing being in the jungle to being in a room - you cannot see through the walls except where there is window - in this case the window 13 ande in the jungle wall" where some land has shipped away taking the trees with it. follow the line of Least resistance to take the
RIES
*
way out which means struggling the legat - that,
the easiest way.
is,
Bentic to become noisoned or to fester, Impediment - something which stops you from doing
that you want. terrain
-
the surface of the land inadvertantly - to do something without realizing
you are doing it.
by adding the case, AB <AC. The proof is then
Completes.
EXIBLE £) K is the mid - point of the diagueal an of the`
pandrilateral ABCD. Prove that the difference between the areas of to turce the area of
A ABC ADC is equal'
Prock: Let AC cat BD at N
(0) Suppose N très bahueen KYD
Can whowán 2 -
* KSA, KDA OM E equal! basea (BK«ks) and of the
Same alfitude -
AKBAS AKDR
<< Atc.
Vokáš - «AND = ARDA - A AND» «ÄKN
KË. SHBA - «ÄNDA 2. AÁKN
Similady. ANBC - ACNDS Z- OCRN
Adding - ABC − & A¢Þ¬ 2. BACK
Do If N lies bekueen
B and K
Then, « ABC < ASACD
Hence, A ACD - SABC === 2. & AKC Consequently, the difference between the areas of as ABC, ADC equals 2 AKC
EXAMILE 3, (8) In a ABC, AB =S", 80=6”. «A&C= 45* Calculate the area of a HBC and the length of AC
J
(b) ABCD is a quadrilateral in which sh=18x4 AB=6** B¢°=10", AD=18". Prove that BD, bisects, « ADC.
SOLUTION: (as Draw-AD LBC
• ABD: LÄDB = 40′′
* 8 = 4.5+
Const.
BAD = 180°- €9%*+ 45*)
== 4-5*
sc 5 son of 10)
BDAD (sides app más)
By Pythagoras, & AÐ2=AB*=5*
*'. Að m -A
Hence, arta of = RBC =‡(AD) (BC)'
4. MADE
=4(√) (6))
驗
DC = BC - 86 = 6
Pythagman, AC1m AÐ2+ Þet
A
Hints & Ans. To
O, Dast in-centre and
ex-centre of a ABC
AOD is a st. line
DOA. FAE are the inh a
ext. angle bisectors of an.
~ DOALFAE
DOA is an altitude of ▲ DEF.
Similarly, E08, FOC are attitudes
* of intersect at 0. the orbacentre of aDEF
LIBR
qiluce HA to K Such that AK = BC
4 BDC = < ABK (SAS)
d = b.
Similarly
d+ b1 = b+b, ade
CDI BK
BF L K C
• KH, BF, CD are attitudes of ¿KBC. 14. AH, BF CD are concurrent
cat the ormocenke of MRUĢI,
By hat the 1 bšectas of AB, BC, AC river at O
•
"
- AB, AD, B7 AC, AD, CD
“: P lies on the 4 biseolar of AB und
- Q lies in the L bisecta of AC. (.. P. Q both coincide wird o NOTE: In a Circle, the 2 bisects of A
a chord passes thru the cenke -
So all the 1 bišteles are concurent at 0 Cushich is the centre of the given circle).
Join BD.
TQD LDC jobŵproducat LAB' @B4 BC 280 produced & AÐ ie, a is the orthocentre of a ABD,
AG LBD
EXERCISE 23
↳ Find the area of a triangle whose sites are (p^-32
Gite reaS UNË,
4. In MABC, 85 = 8 cm, A¢ = ? om,' and p is a point on 8C such that 20=f&c. If the men of MBBC is 24q. cm, find the distances of D ́from AB and from AC, DAPOR 1 A rectangle in which AP»4", ARail”, 8 Cum pt in QR, QP resp. such that RB=3", QC=8= Calculate, as the area of mABC da the length of the line joining the mid-points of 88 and 60% 4. As shown in fig., Q is any
on AC. Prove "that
XXRAD SAYB
point
Paper 23
A, Supoly suitable prepositions.
1. The waves dashed
the rocks.
2. The little boy dashed the toy
3. It suddenly dawned
to say.
pieces.
me what he was going
the
4. The player sitting next to me dealt
cards.
5. The manager deala kindly
6. He deals
7. He took delight
8. I defer
9. I have decided
his employees,,
long walks.
T
precious stones.
My parents opinions.
course of action.
LO. I took my brother's side
B. Punctuate the following passage ›
the argument,
this morning i saw jane on the way to school she was in car no xx3465 a nill van 1 think she didn't sen me as I was in a tram but har brother did he called to me robert robert and waved to me 10 waved back but the car was gon before jane saw us.
6. Put the following into indirect or reprted speech
"Can it be true?" said Defarge.
"As be said it," returned madame, it is probably
false. But it may be true."
"If it is.” Defarge began, and stopped.
*If it 19?" repeated his wife.
·
and if it doe's come, I hope destiny will keep her husband out of France."
•
D. Supply the correct tense of the verb in brackets.
1. If you asked him he
(to come) (leave) at 10 pm. tonight, (to finish) just her work when i
2. My olane
3. She
entered the room.
4. After 1
(search) for half an hour 1 gave it up for lost. 5. He
(to be) not here, when i came. 6. Don't tell lies or you.
(to punish). .7. It
(to rain) continuously for the last three hours.
8. If ne 19 good his mother
an ice cream.
9. !
10. 1
ago.
(to buy) him)
(to live) in Hong Kong all sy life, (to be born) in Macau sixteen year