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12 ;" " 6 ;" No, try again ": 3 ;"three questions." 3 ;"WELL DONE!": 3 ;"Question ";j 3 ;" You obtained ";m;" marks out of 3," 3 ;" Not too good, you need to work": 3 ;" No. Try again ": 3 ;" No, try again ": 3 ;" In a right angled" 3 ;" Now, try a short exercise of" 3 ;" In a right angl-" 3 ;" Find the length" 3 ;" " 3 ;" ";: 3 ;" ": 3 **the exercise** 3 **set up question array** 3 **clean lines** 3 ***CORE*** 3 " questions.": 3 " ed triangle ABC," 3 2 logo 2 file 2 Recording 2 ;"When you are ready to go on to": 2 ;"UPPER CASE"; 2 ;"Type in file name in "; 2 ;"That was not bad!": 2 ;"Stop and rewind tape" 2 ;"SAVE""file"" LINE 2" 2 ;"PRESS S" 2 ;"PRESS R": 2 ;"PLEASE WAIT"; 2 ;"NEW followed by": 2 ;"Load main program" 2 ;"Leave tape running" 2 ;"LESSON TWO" 2 ;"Bye for now!": 2 ;". Therefore" 2 ;" to one decimal place,": 2 ;" to calculate the length of the" 2 ;" AC=";h;",so AC 2 ;" LOADING PROGRAM 2 ;" ": 2 ;" ": 2 ;" " 2 **teaching section** 2 **example** 2 **ending routine** 2 "clear (y/n) ?";q$ 2 "address ? ";x 2 "Filename",a$ 2 " through another exercise of 3": 2 " the area of the" 2 " square root of ";h^2 2 " otherwise:-": 2 " hypotenuse AC.": 2 " formula-" 2 " decimal place." 2 " correct to one" 2 " and the hypoten-" 2 Q 2 " 2 1 s$=s$+A$(k) 1 PYTHAG2 1 PYTHAG1 1 Created with Ramsoft MakeTZX 1 =64+36=100, so AC=10.": 1 ;"we can use the" 1 ;"was equal" 1 ;"of the": 1 ;"Yes, again there are 8 tiles." 1 ;"Yes, 8 tiles make up the square." 1 ;"Would you like to see the proof again? (press Y or N)" 1 ;"What is the total number of tiles in the two smaller squares?": 1 ;"Turn to chapter five in the" 1 ;"These tiles were laid in the" 1 ;"Then he noticed that a square" 1 ;"The computer uses the notation" 1 ;"The Greek found this was true" 1 ;"That was quite good!": 1 ;"That completes the proof.": 1 ;"That completes Lesson One, in" 1 ;"That completes Lesson Two." 1 ;"THEOREM": 1 ;"THE THEOREM" 1 ;"THE AREA" 1 ;"Rectangle" 1 ;"PYTHAGORAS" 1 ;"PYTHAG3"; 1 ;"PYTHAG2"; 1 ;"Now the Greek wondered if this" 1 ;"No,there are 8 tiles,4 in each square.": 1 ;"No, there are 8 tiles.": 1 ;"No, count them!" 1 ;"No, count them carefully.": 1 ;"Measure the sides of the" 1 ;"LESSON TWO": 1 ;"LESSON ONE": 1 ;"LESSON ONE" 1 ;"It is a RIGHT ANGLED" 1 ;"Is the area of the" 1 ;"In each case answer the ques-" 1 ;"In a right angled triangle ABC" 1 ;"If you would like to go over": 1 ;"If you would like to go over": 1 ;"How many tiles make up the square? ": 1 ;"He then noticed that two" 1 ;"BC= cm.": 1 ;"AB= cm.": 1 ;", then correct to" 1 ;", then BC is the" 1 ;", then AB is the" 1 ;"(this is equal" 1 ;" were introduced and used to" 1 ;" we are left with" 1 ;" to mean 5 1 ;" to find the length of the side" 1 ;" to find the length of the base" 1 ;" to calculate the length of AB," 1 ;" the square on the" 1 ;" has the same area" 1 ;" from the" 1 ;" You still do not seem to have": 1 ;" We name the theorem after theGreek thinker named Pythagoras,though it is doubtful whether itwas he who actually discoveredits truth." 1 ;" We can write this as a formula" 1 ;" We can see then, that "; 1 ;" We can now rewrite the theorem" 1 ;" We paint the smaller rect-" 1 ;" Turn to chapter five in the workbook where you will find exercise 2c which contains questions similar to the ones you have just been doing." 1 ;" Turn to chapter five in the workbook where you will find exercise 2b which contains questions similar to the ones you have just been doing." 1 ;" Turn to chapter five in the workbook where you will find exercise 2a which contains questions similar to the ones you have just been doing. The example will be displayed again on the screen to help you in the setting out." 1 ;" Turn to chapter five in theworkbook where you will find anoutline of a right angledtriangle, squares and construct-ion lines. Find the areas of thetwo rectangles and the squaresand so confirm the proof in thatparticular case." 1 ;" This square is the same as the" 1 ;" This red rectangle has the" 1 ;" This parallelogram has the" 1 ;" Then we can call" 1 ;" Then we draw a square on the" 1 ;" The parallelogram has the same" 1 ;" The other rectangle": 1 ;" The long side of a right angledtriangle is usually called theHYPOTENUSE of the triangle, sowe can restate the theorem ofPythagoras:" 1 ;" The Greek noticed that if he " 1 ;" Still not very good, you had": 1 ;" Still not good, but you had": 1 ;" So, if a square has a side of" 1 ;" So, we can divide the big" 1 ;" Similarly we can produce the" 1 ;" Rectangle "; 1 ;" One rectangle": 1 ;" Now we will put the theorem to" 1 ;" Now we draw squares on the" 1 ;" Now look at the other rect-" 1 ;" Next we draw in a construction" 1 ;" In this section you will learn" 1 ;" In this case AB=8 and BC=6, so" 1 ;" In this case this rectangle" 1 ;" In the last section you were" 1 ;" In this section you will beshown a demonstration or PROOFof the theorem for any rightangled triangle." 1 ;" In Lesson Three you will see" 1 ;" IN A RIGHT-ANGLED TRIANGLE, THESQUARE ON THE HYPOTENUSE ISEQUAL TO THE SUM OF THE SQUARESON THE OTHER TWO SIDES." 1 ;" IN A RIGHT ANGLED TRIANGLE," 1 ;" First, we draw a right angled" 1 ;" But this square has the same" 1 ;" BC=6, so BC 1 ;" BC=4cm,so BC 1 ;" BC=";q;"cm,so BC 1 ;" BC=";q;",so BC 1 ;" AC=12,so AC 1 ;" AC=11,so AC 1 ;" AB=8, so AB 1 ;" AB=6cm,so AB 1 ;" AB=";p;"cm,so AB 1 ;" AB=";p;",so AB 1 ;" A PROOF": 1 ;" has the same area as the " 1 ;" You learned to use this form-" 1 ;" So if we subtract" 1 ;" Now we will use the formula:-" 1 ;" Many of the major discoveriesin mathematics have come fromidle observation and the suddennoticing of a pattern. Althoughwe do not know for certain, itis possible that the theorem ofPythagoras was first suggestedto a Greek some 2500 years agowhile he was gazing at thepatterns in a floor made upfrom triangular tiles like this-" 1 ;" Let's put these formulae to" 1 ;" Just as we could use the" 1 ;" In this section the formulae-" 1 ;" In this lesson you will learn" 1 ;" In Lesson One you were shown" 1 ;" ISOSCELES triangle." 1 ;" First an example using the" 1 ;" Do you remember" 1 ;" As you know the area of a" 1 ;" So AB 1 ;" If we draw a" 1 ;" Therefore BC=8.9cm.": 1 ;" Therefore AC=7.2cm.": 1 ;" Therefore AB=9.2cm.": 1 ;" ": 1 ;" ": 1 ;" ": 1 ;" ": 1 **two tile triangle** 1 **triangle** 1 **the proof** 1 **summary of lessons 3** 1 **summary of lessons 1 or 2** 1 **shear 2b** 1 **shear 2a** 1 **shear 1b** 1 **shear 1a** 1 **s-square** 1 **question find side** 1 **question find hypotenuse** 1 **question find base** 1 **number string to 1 dec pl ** 1 **lesson summary** 1 **input a string** 1 **h-square** 1 **fill rect2** 1 **fill rect1** 1 **fill in side square** 1 **fill in s-square** 1 **fill in hyp square** 1 **fill in base square** 1 **fill in b-square** 1 **example two** 1 **draw triangle-hyp&side** 1 **draw triangle-hyp&base** 1 **draw triangle** 1 **draw triangle and squares** 1 **draw tile pattern** 1 **draw tile net** 1 **draw single tile** 1 **concatenation of a string** 1 **check input of a string** 1 **check input a number 2 digits** 1 **c-line** 1 **bookwork** 1 **bookwork 2** 1 **bookwork 1** 1 **b-square** 1 **Exercise** 1 **Exercise 2** 1 **Exercise 1** 1 "Type in y(es) or n(o) ";A$: 1 " yellow square...": 1 " would work in the case of" 1 " work....": 1 " work through this Lesson again": 1 " where you will be shown an- other example.": 1 " where angle ABC is the right" 1 " using letters to label the" 1 " use AC=12. Find" 1 " use AC=11. Find" 1 " use AC correct to" 1 " up a THEOREM.": 1 " understood, so I suggest you": 1 " ula to calculate the length of" 1 " triangles with squares drawn" 1 " triangle...": 1 " triangle.": 1 " triangle ABC,BC=6" 1 " triangle ABC,AB=8" 1 " triangle ABC,AB=6" 1 " triangle AB, the" 1 " to the square on the side AB.": 1 " tion: "; 1 " through another exercise of 5": 1 " three different right angled" 1 " theorem and it was then re-" 1 " the side BC.": 1 " the other two sides.": 1 " the next lesson we shall see" 1 " the length of the" 1 " the length of one of its sides.": 1 " the length of BC.": 1 " the length of AB.": 1 " the hypotenuse and the other" 1 " the base AB.": 1 " the base of this" 1 " the hypotenuse of a right" 1 " stated as follows:-": 1 " squares?": 1 " squares could be made up on" 1 " squares and calculate their" 1 " square on the side" 1 " square on the base" 1 " square into two rectangles...": 1 " square into two rectangles "; 1 " square is found by squaring" 1 " side using a formula derived" 1 " side of the triangle.": 1 " side BC in a right angled tri-" 1 " side BC and the" 1 " shown in Lesson 1,": 1 " same area as the square...": 1 " same area as the red parallel- ogram, for it has the same length and height." 1 " right angled triangles.": 1 " right angled triangle.": 1 " right angled tri-" 1 " right angled triangle ABC" 1 " rectangles.": 1 " pattern shown above.": 1 " other two sides...": 1 " other right angled triangles.": 1 " oras can be expressed as a" 1 " one decimal place,AC is cm." 1 " on their sides.": 1 " on the hypotenuse" 1 " of the triangle.": 1 " of the other two sides of a" 1 " of the square on" 1 " of the areas of the other two" 1 " of Pythagoras was discovered." 1 " of the side BC" 1 " of the hypoten-" 1 " of the base AB" 1 " may be applied to solve" 1 " make up a larger right angled " 1 " long side of the triangle...": 1 " llelogram...": 1 " line which divides the large" 1 " lengths of its other two sides.": 1 " length 5cm, then its area is" 1 " learned.": 1 " its corners A, B" 1 " hypotenuse given the lengths" 1 " hypotenuse AC,": 1 " hypotenuse AC, the side BC or" 1 " hypotenuse AC was" 1 " how to work out the length of" 1 " how these formulae and methods" 1 " how the theorem can be put to" 1 " how it is thought the theorem" 1 " how to use the theorem to" 1 " how in the proof" 1 " has the same area as the para-" 1 " given a more convenient form" 1 " given the lengths of the" 1 " from the one you have just" 1 " formulae-" 1 " formula:- " 1 " formula:" 1 " for the theorem of Pythagoras" 1 " for all the right angled tri-" 1 " find the base or side of a" 1 " equal to the area" 1 " divided into two" 1 " different problems involving" 1 " demonstration proof for the" 1 " could be made up on the longer" 1 " corners of the triangle:-": 1 " combined two tiles, he could " 1 " calculate the length of the" 1 " booklet where you will find" 1 " blue square...": 1 " big square the same as the sum" 1 " better work through the lesson": 1 " better go on with the lesson": 1 " as the yellow square...": 1 " as follows:-" 1 " areas.": 1 " area of the square" 1 " area as the square...": 1 " area as the square on the side" 1 " angles he studied, so he made" 1 " angled triangle given the" 1 " angle.": 1 " angle. First we colour it red.": 1 " angle, the theorem of Pythag-" 1 " angle red...": 1 " angle and label" 1 " and C...": 1 " and BC=4. Find" 1 " again.": 1 " a side given the lengths of" 1 " You were then given a" 1 " TRIANGLE IS EQUAL TO THE SUM " 1 " THE OTHER TWO SIDES. ": 1 " THE OTHER TWO SIDES. ": 1 " THE AREA OF THE SQUARE ON THE" 1 " THE AREA OF THE SQUARE ON THE " 1 " SQUARE ROOT of 85, that is ": 1 " SQUARE ROOT of 80, that is ": 1 " SQUARE ROOT of 52,which is ": 1 " SAME AS THE SUM OF THE AREAS" 1 " OF THE OTHER TWO SQUARES.": 1 " OF THE AREAS OF THE SQUARES ON" 1 " OF THE AREAS OF THE SQUARES ON " 1 " OF THE LARGE SQUARE IS THE 1 " Lesson One again, ": 1 " LONG SIDE OF A RIGHT ANGLED " 1 " LESSON TWO type:-": 1 " LESSON THREE type:-": 1 " LESSON TWO again, ": 1 " HYPOTENUSE IS EQUAL TO THE SUM" 1 " AC=";h;"cm, BC=";q;"cm.": 1 " AC=";h;"cm, AB=";p;"cm.": 1 " AC (equal to AC 1 " AB=";p;"cm, BC=";q;"cm.": 1 " AB (equal to AB 1 " 1 decimal place." 1 " - but not straight away!": 1 is 52, then AC is the" 1 which is 5x5=25cm 1 is 85, then AB is the" 1 is 80, then BC is the" 1 is ";h^2 1