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INVESTIGATION
1.1 Work in a group but start on your own by drawing three right–angled triangles of different shapes and sizes. Work as accurately as possible. It will be a lot easier if you use squared paper. Now work even more accurately and measure the three sides of each triangle to the nearest millimetre. Complete the first three rows of the table. Now use your calculator to complete the rest of the table.
SYMBOL | TRIANGLE A | TRIANGLE B | TRIANGLE C | |
Length of the shortest side | a | .................... | .................... | .................... |
Length of the medium triangle | b | .................... | .................... | .................... |
Length of the longest side | c | .................... | .................... | .................... |
Square of the length of the shortest side | a ^{2} | .................... | .................... | .................... |
Square of the length of the medium side | b ^{2} | .................... | .................... | .................... |
Sum of the two squares above | a ^{2} + b ^{2} | .................... | .................... | .................... |
Square of the length of the longest side | c ^{2} | .................... | .................... | .................... |
1.2 There should be something interesting about the shaded cells of the table. In your group write down carefully what you notice and (if you can) why it happens.
2. Take three lines:
Cutting–out:
2.1 Can the three given squares be used to form a triangle?
3 Write a neat summary of the results of the investigation.
end of INVESTIGATION
The Theorem of Pythagoras goes:
The importance of the Theorem of Pythagoras is that we use it in two ways: Firstly, if we know that a triangle is right angled, then we can say something very important about its sides. Secondly, if we know that the three sides of a triangle have a certain relationship with each other, then we also know that the triangle must be right–angled.
CLASS WORK
1 We label triangles as follows:
REMEMBER always to use a ruler for good sketches!
2 Problem : AEH has a right angle at H.AH = 6cm and EH = 8cm.Draw a sketch (not accurate) of the triangle and use the Theorem of Pythagoras to calculate the length of side AE.
Solution : Because we know that the triangle has a rightangle, we are allowed to say that AE ^{2} = AH ^{2} + EH ^{2} (or: h ^{2} = e ^{2} + a ^{2} )
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