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日一卅月三年〇七九一曆公年九十五國民華中育教

僑

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O英文中學會考試題預習專欄

Value of the difference

In (3) |_ B~~C means the difference

between / B & C (greater aubtract

smaller).

Example 21 AB 18 a side of an n-sided regular polygon.

Find the condition for an other side of the polygon parallel to AB.

Solution: Demote the polygon by ABCD .......MN..

Let UN "be the ith side

Join AN

堅道英文書院主編

數學科

( #~)

ABCD AKT is therefore (x + 1) − sided polygon int. In sun of ABCD..UN

MATHEMATICS (22)

4] rt.L

Sines

• ABCD ....MN polygon is itself an n-sided regular polygon

Important theprams for reference ons

A) Ext. & int. /of a polygons

The int. 8 sum of A (is equal to 2rt./s)

Ext. L of ▲ (equals the sum of int. opp.

3) Lat,

sun of an n-sided polygon (2n

4) Ext. a sum of an n-sided polygon (4

B) Parallel lines:

社

19英文中學會考試題預習專欄

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ENGLISH LANGUAGE (22)

Answers to Exerclas ZL

1. (C) up

2. B) out 3. (D) thro

4. (C) off

5. (C) out

-6. (a) up

8. (B) up

7. (C) dowa

9. (B) out

10. (D) OveR

11. (D) belief

12. (A) ingenious

13. (D) nenosnitates

14. (B) momentous

19. (A) devoured 20. (B) offads. 21. (B) Boeing 22%

Aran

23. (C) would not have won 24. (0) on his arrival 25. (B) entering the housa 26. (A) the door being opened 27. (C) only ould be give us

help

28. (D) No 8ORST

29. (5) should have finished 30. (C) had been working.

31. (A) it is strange to have

дом

32. (A) it is possible that he is} 17. (0) apologetia e not tipted 18. (0) oczomically 33. (0) I would do everything to

34.

make all of you happy one should be practical

should offer our help properly

22-4 st. L

LB • LC

20-4) (x + 1 2(n − 2)(x-1)

2)rt.

And

. (int.L, AB//XX} 2(a−2(x+1) int, um of ABCD..MM

15. (4) continuous

16. (3) wagon

+ 2 ... (2)

5)

o fundamental Axions

Two coplanar st. lines are eliner intersect or parallel.

Two intersecting coplanar st. lines cannot both be parallel to a third at, line, (Playfair's Axiom)

If either (a) alt. / 1 oqual,

(b) DOTT.

equal, or (c) int, Zai supp., then the two st. lines are parallel.

7) ££ ■ ■t, line outs two or more parallel

lines then (a) alt. / ■ equal, (b) corr. equal, (0) int. 8 supp.

or more st. lines which are parallel to the same st, lines, are parallel to one another.

9t, lines which are perpendicular to the same coplanar at. linea, are parallel to one another,

In a parallelosame

10) Opp. miden, (gram (are equal)

gram (are equal)

12) diag. gram (bisects each other) 13. diag. of // gran bisects the // gran inte

two congruent triangles.

quadrilateral to be a parallelogramı

14) opp. aides equals or

15) opp. £s equal; or

16) ding. bisect each other i

17) a pair of opp. sides

Theorems on other properties of a quad.

18) Restangle, square and rhombus are //grun

Bush that

(1) for a rest,1 the diag, are equal and

· binëot exach other.

(b) for a square; the diag. are aqual and

bisect each other at rt. (») for a rhombues the diag, are unequal,

but bisect each other at

In an isos, trapeglunt

the diag.. are equal ş the base. are equal.

[N.B. Reot. •//gram + still

Square - sect. adj. sides

Rhombus w//gran + adj. sides equal,

EXAMPLES †

Example 11 In ABC, prove that the angle formed

by the altitude with the angle bisector

et A, equals half the difference of

B and C.

Given: ABC with ADLBC

AB bisects BAC

2

Eq. (1) and Eq. (2) are identical (same int./ cum)

2(x − 2)(1 − 14, 2 = 2x

n

− 2)(x − 1) + n = (x − 1)a

1

Which is meaningful, only when n is even; in other worde, no parallel sides for an odd-sided regular

Proofs

30

le shown in fig., ABCD is a square, LAPB

PB = **•L CXQ//AP, DQ//BPX. Prove

that (1) PX - AP.

- (2) LAPQ

AP //

_BXC » BPA = 1

BUR of A

ABP:

· LAPB = 1 T+iL__ Proved

Proved

(siden of square

ABCX = A ABP (AAS)

BX - AP (COTT sides of=A.)

-BX-BP

BP

[Similarly, we find

FB

4

ABP ABCX= CDQ (AAS)

FOX 18 1200oslos and right-angledɛntɛ zi QPI = 45%

Example 41 ABD, ACE are equilateral As on 43, AC of

▲ ABG, DAEF is a //gram outside Prove that FBC is also an equi,

Fy (a)

Fig

Exercise 22

Precisi

Read the following passage carefullys

It is not easy to define luxury. It is'n word whose meaning shifts and changes like the shape of a mountain in a driving mist. To the political economist, luxuries are all things which are not necessary to life and efficiency, and therefore they include many things, not only innocent, but very desirable. But to a Puritan preacher, luxury was of the devil, and a temptation to mortal ain. Koreover, luxury is not an absolute idea; we cannot say of any particular thing that it is in itself a luxury, For what is a luxury to one class of people, or in one country, or in one period, may be a necessary to another class, in another country, or another period.

luxurias to the grandfathers become recensaries to their grandsong.

MAAL the standards of living rise, things that were

As the economiste classify things as necessaries and luzuries, perhaps it will help us to a definition of the latter word, if we cohmider necessaries for a minute. Necessaries for life and efficiency are a sufficient quantity of wholesome food, warm clothing, fuel and shelter. If a man has these, he can not only maintain life, but keep physically fit. But can any man, except the poorest, be content with only such bare necessarios? The Bible says, "Mạn doth not live by bread along." Man is not a mare animals he has a mind and a soul to feed as well as a body. And for real living, as distinguished from mere existence, many other things than food and slothes and a house and fuel are necessary. And the higher the standar/

of life to which any particular man has become accustomed, the greater the number ad variety of things that are necessary. A child brought up in a poor working-man's home is quite confortable and happy with very few things; but a boy reared in a well-to-do family becomes so accustomed to a certain standerd of house, furniture; meals, dress, servants, and various conveniences, that he would be absolutely miserable if he were compelled to live in a working- class family. These things, which to the poorer man would be luxuries, are, therefore, to him real necessaries; for though he might exist without them, he could not live (in the fullest some of the tern) without them.

Again, the tastes of individual men differ widely. To an eager scholar, books (which to many men are luxuries and quite unnecessary) are more necessary. aven than food and drink and shelter; and many a atudent would rather go without a fire on a cold) night than deprive himself of his books.

(未完轉入第六張第三頁)

BC BE

Similarly BO CF

corr. sides of Δ

ABC

ETC

To prove: / DAE = $148 - LC/

Proof: In AABC, if /B> __C

LBAB

BAS-BAC,

- 1/ BAC - (90° - ___»)

180°-B

\_C)− (90° - __B)

· † (⁄ 3 − / ©)

Conversely, if | B</ C, then E lies between 3 and] D. Hence,

LB)

[In particular, when ___B = /_C___

[Givent As ABD, ACE are equilateral

ADFE in a // grER

To Proves FEC is na equi. Proof: Let BAG - £

Then, DAR 60 + 60

120944 (In rig. bi / DAR – 240o

/ FDA - 180° - __ DAB

180° 600.

(In fig.

Alad an iron.

▲ FBC is equilateral

Example 5 The diagonals of rect. ABCD cut at K, and AK is greater than AB. The circle, centro A, radius AK, cuta AB produced at E. If ZAKB 4/ BKB, find

Given: Reot, ABCD

AK

BAC

(Am in fig.

AF

(120° + ∞) in f

60°) both fig. ap

KA

In A ABK, +

Fo finds m

Solut

AD

(Given)

+

K-5k (base LB 1808 A)

5k2 (ext. L of A

KB (diag. of rest.)

6K2

(bane L, 1198 A)]

-180° 6K2 + 6k2 +

4

180

HLB - LB)

Consequently

NOTE: We may uns (n) /LB - __c/ ox (8) L3~20}

to denote the difference

In (a), / £8 - / C / represents the absolute

Hence, in A • ABC, DUY

AC - DF (-15) (sides of equi.

opp sidas, // izan)

Z_BAC - / BDF (= 2 )

-AB-DB

ДАВС

Froved

- wides of equi. A A DB

SAS:

Hence,