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10 "9";"Press any key": 9 "0";"What is the"; 8 "8878"*(ind= 6 sc 6 >::>>>>>>>>99>>99;;>>>>>>>>> 6 >::88::88>>99;;9>;;99;;9>;;> 6 >::88::88>>99;;99;;99;;99;;> 6 ;" Program loading "; 6 ;" PLEASE WAIT "; 6 "0";" STOP TAPE & press ENTER ": 5 o$=" ": 5 * WELL DONE * 4 j;". ";p$(i): 4 ;"SOFTWARE 4 "7";"YOUR ANSWER No. ";q$: 4 "6";"MORE EXAMPLES? y OR n": 4 PRESS KEY 4 EXERCISE 4 Correct answer is no. ";k: 3 gr 3 A.Cowley Apr.1983 3 "17";e-g;" 3 "0";o$;o$;o$; 3 TOTAL INCORRECT: 3 REVISION QUESTIONS 2 s and 1 side (AAS) 2 gr ( 2 "0";"value of the"; 2 "0";"value of 2 "0";"triangles"; 2 "0";"parallelogram?" 2 "0";"interior angles"; 2 "0";"These two"; 2 "0";"The radius of the"; 2 "0";"AC is a diameter"; 2 lines or lines of symmetry 2 are ALTERNATE 2 The diagonals are NOT mirror- 2 TOTAL INCORRECT: ";v: 2 TOTAL CORRECT: 2 A 2 1 since c and "+ 1 since a and "+ 1 s of a quadrilateral = 360 1 s in cyclic quad.) 1 s OF CYCLIC QUAD=180 1 s OF A TRIANGLE = 180 1 q$="t");("false" 1 p$="t");("false" 1 o$=" " 1 k+" =OPxOQ=OPx(OP+"+ 1 i+"=2x6 so PN="+ 1 gr 0 1 g6 ` 1 g5 q 1 g4 q 1 g3 q 1 g2 q 1 g1 q 1 four two eight AF 1 f$="(omit 'cm')": 1 f$="(omit 1 a$="since d="+ 1 a$="since a/b = "+ 1 a$="since "+ 1 a$="RUBBISH" 1 a$=" 1 a and b are CORRESPONDING ANGLES 1 TZXed by Andrew Barker 1 TYPICAL 'O' LEVEL QUESTIONS 1 THIS IS NOT PROOF OF CONGRUENCY 1 SUM OF OPP. 1 Rose Software 1 QRS = ";90 1 QOS from previous question": 1 PUT n=4 INTO (2n-4)X90 1 PQS) QS (from 1 Original Release 1 O is the centre": 1 MORE EXAMPLES? y OR n": 1 Geometry 5 1 Geometry 4 1 Geometry 3 1 Geometry 1 1 Educational 1 DAE=180-50-"+ 1 CRQ is isosceles ": 1 CQR=";(180 1 CORRESPONDING 1 CORRECT ANSWER";: 1 CEF=90-40= 1 CAB=180-"+ 1 BCD (alt.seg.th.) 1 ABC through 120 1 ABC is isosceles": 1 ABC IS ISOSCELES & 1 A.Cowley Mar.1983 1 =OPxOQ SO "+ 1 ;" x ";j^2 1 ;" SEGMENT THEOREM 1 6 1 5 Y 1 4 1 1 3 * 1 2 1 1 1 /i)+" and OT 1 +j;" such","rotations, A",,"returns to its",,"original position" 1 *j*i;"cm": 1 *j);" sq.cm" 1 *i;"cm->"; 1 *i)+"=QR/PQ giving PR="+ 1 )="yXz=360 1 )="y+z=180": 1 )="y+z=180 1 )="vertically opposite angles": 1 )="trapezium": 1 )="supplementary (a+b)=180 1 )="rhombus": 1 )="rectangle": 1 )="parallelogram": 1 )="hX(a+b)/2": 1 )="eight": 1 )="corresponding angles" 1 )="complementary (a+b)=90 1 )="c=a+b": 1 )="b=c+a": 1 )="alternate angles": 1 )="a=b+c": 1 )="OT=OS": 1 )="OT=2 x radius": 1 )="OT+OS=2x 1 )="OP=half radius": 1 )="OP = AP": 1 )="90+y=z": 1 )="360/y": 1 )="360/(180-y)": 1 )="(aXh)-b/2": 1 )="(aXb)/h": 1 )+"x("+p$(2 1 )+"+2r) 1 (omit 'cm')P 1 #'O' Level Maths Revision - Geometry 1 "9";"Press any key" 1 "8";"similar triangles.": 1 "8";"(tangents CR=CQ)": 1 "7";"YOUR ANSWER: ";("true" 1 "7";"CORRECT ANS: ";("true" 1 "6";"subtended by arc QB)": 1 "5";"Compare the sides of the"; 1 "4";"similar (equal angles)": 1 "4";"FOR AN"; 1 "4";"(from previous question)"; 1 "4";"(angles in same segment"; 1 "3";"Triangles PQS and QSR are"; 1 "3";"QS = ";k;" x ";j;" = ";k*j;"cm": 1 "28";"<-";i; 1 "27";"-->" 1 "26";i;"cm"; 1 "23";i;"cm"; 1 "23";"ext 1 "23";"<-a->"; 1 "2";"(alternate segment theorem)": 1 "2";" So ": 1 "2";" END ": 1 "19";"<-b-> <-a->" 1 "19";"<--"; 1 "18";"<---- b ---->"; 1 "17";i;"cm"; 1 "17";i;" cm"; 1 "17";"SR"; 1 "17";"<-";2 1 "15";"= --"; 1 "14";"ROSE"; 1 "12";"SOFTWARE" 1 "12";"SOFTWARE 1 "12";"QS ";j^2 1 "12";"-- = --"; 1 "1";"c'?": 1 "1";"b'?": 1 "1";"Your answer: ";a$: 1 "1";"INTERSECTING": 1 "1";"INTERNAL POINT"; 1 "0";o$;o$; 1 "0";"z=?": 1 "0";"y is the angle"; 1 "0";"y and z?": 1 "0";"y and z are"; 1 "0";"value of "; 1 "0";"true that:-" 1 "0";"true for"; 1 "0";"topmost angle"; 1 "0";"to SR"; 1 "0";"this special"; 1 "0";"then it is"; 1 "0";"the sum is (2X6-4)X90 1 "0";"the radius of"; 1 "0";"the area of"; 1 "0";"tangent."; 1 "0";"tangent to"; 1 "0";"tangent is ALWAYS ?" 1 "0";"symmetry for a"; 1 "0";"sum of the"; 1 "0";"states c 1 "0";"smaller circle"; 1 "0";"similar"; 1 "0";"quadrilateral?": 1 "0";"polygon is"; 1 "0";"polygon has"; 1 "0";"or line of symmetry"; 1 "0";"opposite 1 "0";"of the"; 1 "0";"of the circle"; 1 "0";"of symmetry does"; 1 "0";"of rotational"; 1 "0";"of an n-sided"; 1 "0";"of a regular hexagon?" 1 "0";"of a quadrilateral?" 1 "0";"of PR is ";4 1 "0";"of PQ is "; 1 "0";"of ANY polygon = 360 1 "0";"name of"; 1 "0";"name of this"; 1 "0";"m is a mirror line"; 1 "0";"lines of symmetry": 1 "0";"larger circle"; 1 "0";"is true?"; 1 "0";"is bisected."; 1 "0";"inscribed"; 1 "0";"in one interior 1 "0";"in a rt 1 "0";"formula for"; 1 "0";"for this equilateral 1 "0";"following"; 1 "0";"exterior 1 "0";"diameter"; 1 "0";"cyclic quadrilateral"; 1 "0";"circle RPQ"; 1 "0";"circle QRS"; 1 "0";"centre P = ";i/2 1 "0";"centre O = ";i;"cm." 1 "0";"b ";i+j 1 "0";"at the centre"; 1 "0";"are tangents."; 1 "0";"are similar"; 1 "0";"are congruent": 1 "0";"angles marked"; 1 "0";"angle marked"; 1 "0";"angle marked '?'" 1 "0";"and we know 1 "0";"and OP=";5 1 "0";"and APQ are"; 1 "0";"about angles"; 1 "0";"a,b and c?" 1 "0";"a trapezium?" 1 "0";"a rectangle have?" 1 "0";"a circle and a"; 1 "0";"a and b are:-": 1 "0";"a = ";i+1 1 "0";"Which of the"; 1 "0";"What is the order"; 1 "0";"What is always"; 1 "0";"What can we say"; 1 "0";"What are the equal"; 1 "0";"Triangles ABC"; 1 "0";"The sum of the"; 1 "0";"The sum of the internal 1 "0";"The angle z between a chord AB",,,"and a tangent is equal to the",,,"angle z in the alternate segment": 1 "0";"The angle between"; 1 "0";"The SUM of the exterior angles"; 1 "0";"TC is a tangent"; 1 "0";"ST is a"; 1 "0";"SR=";j^2 1 "0";"SO the length"; 1 "0";"PQ=";k^2 1 "0";"PQ is parallel"; 1 "0";"PQ (from 1 "0";"OT and OS"; 1 "0";"OP = ?" 1 "0";"O is the centre."; 1 "0";"NQ=";i;"cm": 1 "0";"NOTE that RQ is parallel to AB since 1 "0";"If the area of"; 1 "0";"If AP=PB"; 1 "0";"If OT=";4 1 "0";"How many lines"; 1 "0";"How many degrees"; 1 "0";"Don't forget there may be more than one HELP per question": 1 "0";"C is the centre"; 1 "0";"By rotating equilateral"," 1 "0";"Angle between tangent and radius": 1 "0";"AQT is a"; 1 "0";"AOB is a"; 1 "0";"AB=";i+2 1 "0";"AB is a diameter"; 1 "0";"A regular n-sided"; 1 "0";"=(12-4)X90 1 "0";"(2n-4)X90 1 "0";"'a' called?": 1 "0";" QUESTIONS 1 ","about P, we get the","same picture" 1 " your answer",f$: 1 " CHORD THEOREM": 1 " (alternate angles)"; 1 y or n ": 1 this irregular hexagon"; 1 the length"; 1 the area of"; 1 perpendicular bisector of AB 1 of cyclic quad. SO 1 of AB and AC 1 making ";3 1 it has ";3 1 in semi-circle) 1 has 3 such lines 1 cyclic quad. 1 between radius & tgt)and 1 atcentre=twice 1 at circumference) 1 at circumference"; 1 at centre & 1 are SUPPLEMENTARY 1 TOTAL INCORRECT: ";v 1 TOTAL CORRECT: 1 THEN opp. 1 So SQ = ? 1 SYMMETRY 1 SUM OF EXT. 1 SUM OF ANGLES OF 1 SO CS=r="+p$(1 1 SINCE OP = OT - PT = "+ 1 SINCE IT IS ONE-THIRD OF 360 1 SIMILAR TRIANGLES 1 Remember P and Q are midpoints 1 ROTATIONAL SYMMETRY 1 REVISION QUESTION 1 REVISION "; 1 REMEMBER THIS:- 1 PYTHAGORAS THEOREM 1 PN x NQ = RN x NS 1 Order of rotational symmetry=3 1 OR NEED help? ENTER h 1 OP is called the 1 OP X OQ = OR X OS = OT 1 OF A CYCLIC QUAD. = THE INTERIOR OPPOSITE ANGLE 1 Like to see why? ";: 1 Hi there 1 HI THERE 1 Geometry 2 1 Geometry 6 1 FOUR TIMES THE AREA 1 Equilateral 1 EXTERIOR 1 DOUBLING THE DIMENSIONS GIVES 1 DIVIDE THE SUM (2n-4)X90 1 CORRESPONDING ANGLE with "+ 1 CONGRUENT 1 CONGRUENCY OF TRIANGLES 1 BY ROTATING 180 1 Always:- 1 APQ is ";i;" sq.cm"; 1 AN EXTERIOR 1 ALTERNATE ANGLE with "+ 1 ABOUT P TWICE 1 ABC is ";i*(4 1 = sum of INT. opp. 1 4 SIDES EQUAL & DIAGS.AT RT. 1 3,4,5 and 5,12,13 are rt 1 2 OPPOSITE SIDES ARE PARALLEL 1 (vert.opp. 1 (must be the included angle)": 1 (angle in semi-circle) SO 1 (alt.seg.th.) SO 1 (See OSBQ)": 1 TOTAL CORRECT: ";u; 1 TOTAL CORRECT: ";u 1 TOTAL CORRECT : ";u; 1 THE ALTERNATE "; 1 SO z=2X"+ 1 ALTERNATE ANGLES 1 3 sides equal (SSS) 1 2 sides & included 1 TANGENTS FROM AN EXTERNAL POINT ARE EQUAL IN LENGTH 1 45 1 180 1 A 1 40 1 30 1 P 1