1969-03-11 — Page 22

AC8B78 BCTALFOCAR WAH KIU YAT PO

1969 ?

文中學

數學科 (十九) 歐陽鐇文

MATHEMATICS (19).

polyg

LESSON 19 Int, & Ext.

Parallelogram.

Important theorems for reference on:

Ext & int

1

of a polygon:

The int, es sum of a (is equal to 2 rti 2: Ext. 4 of (equals the sum of int. opp.

31 Int., sun of an n-sided polygon (2n - 4 rt 4 Ext. ce sun of an n-sided polygon (4 rtze)

Parallel lines:

5: Two fundamental AXIOMS

a) Two coplanar st. lines are either intersect

or parallel.

Two intersecting copanár st. lines cannot

both be parallel to a third et. line. (Playfair's Axion

If either (a) alt, equal, or (b) corr. equal, or (c) int, — supp., then the two st, lines are parallel.

If a st line cuts two or more parallel lines then (a) alt. equal, (b) corr, as equal, fel înt, supp.

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

St. lines which are perpendicular to the same coplanar st. line, are parallel to one another.

郭日僑華

二期星日一十月三年九六九一曆公年八十五國民華中 青教僑華

Since ABCD

polygen

an n-sidat

regular polygon.

1969

CC英文中學會考

題預習

英文科

(十九)

+

And

ABUMN).

MNS

atn-auty a

int. • Sum of ABCD-

Eg(1) and kg(2) are identical (Some int

hich is meaningful only when n is even; in other words, no parallel sides for an odd-sided regular polygon.

xample 3: As shown in fig.

APBrt.z

that(1) PXAP.

(2) ZAFQ=45

Proofi

AP/QC

A, BCX, ABF

BXC

LAPB = 1 +

BC = AB

ABCD 1s a souare CXQ / AP. DG // BPX

Prove

Sum

(V) walls

b (iii) erupt

ENGLISH (19)

Answers to Paper XVIII

(v) wending its way

d. (v) soars

eiv) rend

f111) muttering

11 merrily

h. iii) lamenting:

1. iv) defiance of

j. iv) snugly

Suddenly Lord John, who was walking Iirs

halted with uplifted hand,

Look at this! said he. By tieorge, this must be the trail of the father of all birds!

An enormous three-toed track was imprinted in the soft mud before us. The creature, whatever it was, had crossed the swamp and had passed on into the forest. We all stopped co examine that monstrous spoor. If it were indeed a bird and what animal could leave such a mark? its foot was so much larger than an ostrich's that its height upon the sama scale must be enormous. Lord John. Looked eagerly round him and slipped two cartridges into his elephant-gun.

11 stake my gom name as a shikaree (hunter) said he, that the track is a fresh one. The creature has not passed ten minutes. Look how the water is still oozing into that deeper print! By Jove! See, here is the mark of a little boat?*

(1) of

(2) of

(7) of

(8) of

square

| BCX= 6ABR.

AAS

7(3) from

19) of

·AP

(4) on

(10) with

- BX-BP

45) of

·(6) in

(11) in

parallelogram:

10: Opp. sides, / gram (are equal).

11: Opp. es #gram (are equal

12 i diag. ✔ gram(bisects each other. 13

dlag, of // gran bisects the ran into two congruent triangles.

n) A quadrilateral to be a paral

14: opp. sides equal; Or

15 opp. 4 equal; or

16′′• diag. bisect each other, or

17 a pair of opp. sides

Theorems on other properties of a quad.

Rectangle, square and rhombus are gra

Buch, that

(a) for a rect..

the diag, are equal and bisect each other.

(b) for a square the diag. are equal and bisect each other at rt.

(e) for a rhombus: the diag, are unequal,

but bisect each other at

Similarly, we find

Example

In an isos, trapezium':

rt. 48

(a) the diag, are equal;

(b) the base z, are equal.

In a kite: one of the diag bisects the. other art.es

Rect.gram

Rhombus

EXAMPLES

Given

Square rect. + adj. sides equal.

#gram adj. sides equal

In ABC prove that the angle formed: by the altitude with the angle biseco for at A, equals half the difference. of B and C,

ABC with ADL BO

AE bisects BAC 1.8. a.

To prove

DAE = 110

I A ABC H B

Q1 = <BAE-Q,

BAE÷BFC

Conversely,

A then E lits Bettion.

and. D. Hence

In Dasticular, when «BEC, IR BABE 23 1553,

NOTE: We may use (0) |-8--C] (b)

to denote the difference,

In (a), |<8-«C| represents the absolute

In (b).

Value of the difference

BALC means the differenca between 18+ ac ( greifer subhact

Example 2: AB is a side of an n-sided regular polygon,

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

Solution: Denote the polygon by ABCD. UN

ABCD

int.

Let UN be the xth side

s.f... MNIAB & x an

Join AN

is Hierefore

polygon

sum at ABCD-- MN

[2(X+1)=4] sha = (2x++)shas

APRXS isasceles and right-angles at x

ABD, ACE are equilateral a, on AB, AC ABC, DARF is a gram outside ÄBD Frove that PBC is also an equi.

Fig ca

Given

A ABD, ATE GR ADFE is a ligram Prove: FBC is an epos

lateral

frost

Then,

CDAE

Li figh: DAE

-FDA150

=180°

FDAS ZFDB = ∞ ASC DBF:

AC=DPE BE)

BAC = -BDF (*

AB D&

ADEF BC= 3F BC= CF

Fig.ch:

in bath

(sides of spai a cjy sides, ligiam proved

Sices of egu a

Cor. Sizes ofanz A ABCS AEFC

imikals

AFBC

is

equi lateral

Exanole 5: The diagonals of rect. ABCD cut at K, and AK is greater than AB. The circle, centre A, radius AK, cuts AB produced at E If

- AKB = 4 - BKE, find 2840

Given: Rect, 1BCD

AKAE

Ak

find r

Solution:

AKAE

RAAB

In a ABK a+b+; = 180°

Hence,

=67;

(未完聼入第六張第三頁)

Given

base u 150S A ext 2 of a sting of reat base 2, isos a

sum of

(12) of

Paper XIX

travel in the younger sort, is a part of education; in the elder, a part of experience.ne who travels into a country, before he has some entrance into the language, goes to school, and not to travel. That young men travel under some tutor or grave o servant, I allow well; so that he be such a one that has the language, and has been in the country before; whereby he ray be able to tell them what things ara worthy to be seen in the country where they go, what. acquaintances they are to seek, what exercises or discipline the place yields; for else young men shall go hooded, and look abroad little.. It is a strange thing, that in sea voyages, where there is nothing to be seen but sky and sea, men should make diaries; but in land travel, wherein so much is to be observed, for the most part, they omit it, let diaries, therefore, be, orought into use. The things to be seen and observed are, the courts of princes, especially when they give audience to ambassadors; the courts of justice, while they sit and hear causes, and so of consistories ecclesiastic, the churches and monasteries, with tre monuments which are there in extant, the walls and fortifications of cities and towns, and so the havens and harbours, antiquities and ruins, libraries, colleges, disputations, and lectures, where any are; shipping and navies, houses and gardens of state and pleasure, near great cities; armouries, magazines, exchanges, warehouses, exercises of horsemanship, fencing, training of soldiers, and the like, comedies, treasuries; and, to conclude, whatsoever is memorable in the places where they go; after all which the tutore or servants ought to make diligent enquiry, a f triumphs, masks, feasts, weddings, funerals, capital executions, and such showe, men need not to be put in mind of them: yet are they not to be neglected. If you will have a young man to put his travel into a little. room, and in snort time to gather much, this you must do: first, as was said, he must have some entrance into the language; then he must have suon a servant, or tutor, as was likewise. said let him carry with him also some card, or book, describing the country, which will be a good key to his enquiry; let him keep also a diary; let him not stay long in one city or town, more or less as the place deserves, but not long when he stays in one city or town, let him change his lodging from one end and part of the town to another, which is a great adamant of acquaintance; let him sequester himself from the company of his countrymen, and diet in such places where there is good company of the nation: let him procure recommendation to some person of quality residing in the place to which he goes, that he may use his favour in those things he desires to see or know, thus he may abridge his travel with mich profit. As for the acquaintance which is to be sought in travel, that which is most of all profitable, is acquaintance with the secretaries and employed men of ambassadors; for

so in travelling in one country he will suck t-- experience" of many let him also see and visit: eminent; Dersons in all kinds. which are of great name abroad.

y be able to tell now, une Lue agrees with the fame; for quarrels, they are with care and discretion. to be avoided; they are commonly for mistresses, healths, place, and words; and let a man beware how he keeps company with choleric and quarrelsome persons for they will engage him into their own quarrels. when a traveller returns home, let him not leave the countries where he has travelled altogether behind him, but maintain a correspondence by letters with those of his acquaintance which are of most worth; and let his travel appear rather in his discourse than in his apparel or gesture; and in his discourse let him be rather advised in his answers, than forward to tell stories and let it appear that he does not change his country manners for those of foreign parts; but only prick in some flowers of that he has learned abroad into the customs of his own country.