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Learning about Click to begin… Joe Deevy. It’s a triangle with one 90° angle The 90° angle usually has a square drawn inside.

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Presentation on theme: "Learning about Click to begin… Joe Deevy. It’s a triangle with one 90° angle The 90° angle usually has a square drawn inside."— Presentation transcript:

1 Learning about Click to begin… Joe Deevy

2

3 It’s a triangle with one 90° angle The 90° angle usually has a square drawn inside

4 The triangle’s sides have names:

5

6

7 click on one of the legs:

8 Correct! The legs touch the right angle!

9 No, that’s the hypotenuse – it’s opposite the right angle Try again!

10 click on the hypotenuse:

11 Correct! The hypotenuse is opposite the right angle!

12 No, that’s a leg – it touches the right angle

13 …and what did he do? Joe Deevy Pythagoras teaching

14 Name the legs of a right triangle a and b. Name the hypotenuse c. Pythagorean Theorem: The lengths of sides a, b, and c are related by the equation: a b c a 2 + b 2 = c 2

15

16 Finished!Click arrow to see the next step…

17 What is the length of the hypotenuse c ? Click the correct answer: a) 14 mm b) 10 mm c) 3.74 mm d) 100 mm

18 Correct! c = 10 mm

19 No, the correct answer is b) 10 mm Here’s how you find c : a 2 = 64 b 2 = 36 a 2 + b 2 = c 2 64 + 36 = c 2 100 = c 2 c = 10 mm

20 Joe Deevy Do you remember how to find the area of a square? Area = side 2

21 Joe Deevy Put these squares around a right triangle a 2 + b 2 = c 2 means that the blue and green squares together cover the same area as the area of the red square by itself! How would you prove that?

22 Joe Deevy Click on the movie camera, to see a video:

23 Joe Deevy No Vote by clicking Yes or No: Yes

24 Joe Deevy The water demonstration gives the idea, but: it’s not exact it doesn’t show that the theorem always works Let’s look at a real proof…

25 Joe Deevy The water demonstration gives the idea, but: it’s not exact it doesn’t show that the theorem always works Let’s look at a real proof…

26 Joe Deevy Click on the movie camera, to see a video proof:

27 Joe Deevy Here are two proof demos that you can play with: Proof 1Proof 2 Hint: For this demo, move the pink circle if you like, then use the slider at the bottom of the window to see the proof. Hint: Use the “Start” and “Next” buttons to step through the proof

28 Joe Deevy Congratulations! Now you know what the Pythagorean theorem is all about!

29 Joe Deevy A. Bogomolny, Pythagorean Theorem By Hinged Dissection 3 (Third Interactive Variant) from Interactive Mathematics Miscellany and Puzzles. http://www.cut-the-knot.org/Curriculum/Geometry/HingedPythagoras3.shtml. Accessed 17 July 2010 http://www.cut-the-knot.org/Curriculum/Geometry/HingedPythagoras3.shtml Math Cove - Teaching and Learning Mathematics with Java. http://oneweb.utc.edu/~Christopher-Mawata/geom/geom7.htm http://oneweb.utc.edu/~Christopher-Mawata/geom/geom7.htm. Accessed 17 July 2010 YouTube: Teorema de Pitágoras. http://www.youtube.com/watch?v=hTxqdyGjtsA&feature=related http://www.youtube.com/watch?v=hTxqdyGjtsA&feature=related. Accessed 17 July 2010 YouTube: The Pythagorean Theorem animation. http://www.youtube.com/watch?v=7- BU5y6jZpw. Accessed 17 July 2010 http://www.youtube.com/watch?v=7- BU5y6jZpw

30 Joe Deevy PDE: 2.3.G.C: Use properties of geometric figures and measurement formulas to solve for a missing quantity. 2.9.G.A: Identify and use properties and relations of geometric figures; create justifications for arguments related to geometric relations. ISTE NETS: 4d. Students use multiple processes and diverse perspectives to explore alternative solutions. 5b. Students exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity. 6d. Students transfer current knowledge to learning of new technologies.


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