Pythagorean Theorem Lesson Plan Alvina 8.3

Thursday, April 5, 2012

What is a Pythagorean Theorem?

A Pythagorean Theorem is usually found in a right-angled triangle. The formal definition of Pythagorean Theorem is this

Thursday, April 5, 2012

In a right-angled triangle, each side is labeled with either with a A,B, or C. The longest side (hypotenuse) is labeled C, while the other sides are labeled with either A or B.

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PROVING THE PYTHAGOREAN THEOREM To find a Pythagorean Theorem, we must find the length of side a and b. Then make the numbers to the power of 2 and add it and it equals to C to the power of 2. Then we make it to a square root, which equals C. So here is the solution that students need to remember Thursday, April 5, 2012

Number Problems 3cm

c

3cm

c

4cm 6cm Solution: Solution: 3 to the power of 2 + 4 5 to the power of 2 and 12 to to the power of 2= 25. the power of 2 equals to 169, The square root of 25 is which is the square root of 5. So the solution is 5. 13 Thursday, April 5, 2012

Word Problems John ran in a field that has the shape of right-angled triangle like the one shown below. The A part is 8 m while the B part is 6 m. How much distance does he need to travel in order to go to back to A? c

6m 8m Thursday, April 5, 2012

Solution 6 to the power of 2 + 8 to the power of 2=100. The square root of 100 is 10. The answer is he needs to travel 10 m to get back to the starting point.

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A right-angled triangleâ€™s height is 5 cm and the base is 12 cm. How long will the hypotenuse will be?

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Solution: 5 to the power of 2 cm+ 12 cm to the power of 2 = 144+25 =169 =Square root of 169 =13

The difference between the pythagorean theorem and the converse of the pythagorean theorem is that sometimes it doesnâ€™t have a definite answer, unlike the pythagorean theorem solutions, and the students donâ€™t have to find the C.Some of the triangles are not rightangled. The students have to find out by themselves whether which triangle are right-angled and whether a+b=c. And THEY HAVE TO PROVE IT. Thursday, April 5, 2012

The Converse of Pythagorean Theorem problems includes exercises in which the student have to prove whether a triangle is a right-angled triangle or not.

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Explanation Sample Problem (Taken from MYP 8 Math Textbook): A triangle with the shorter sides of 5 cm and 12 cm and the hypotenuse side of 13 cm. 5 to the power of 2 + 12 to the power of 2 = 169, while 13 to the power of equals to 169. So this triangle is a right-angled triangle.

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Sample Problem Another problem: 3 to the power of 2+5 to the power of 2 =34 While 7 to the power of 2 =49 So this is not a right-angled triangle

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Original Problems

Taken from http://www.redmond.k12.or.us/ 14552011718214563/lib/ 14552011718214563/Lesson_9.2.pdf Thursday, April 5, 2012

Explanation A Babylonian Triple or Pythagorean Triple is a set of numbers(integers) which satisfy the rule a to the power of 2 + b to the power of 2 = c to the power of 2. For example, 3 to the power of 2 + 4 to the power of 2 = 5 to the power of 2.

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To prove whether a set of numbers is a Pythagorean Triple or not, you can find out: (3,7,9): 3 to the power of 2 + 7 to the power of 2=58, where as 9 to the power of 2 equals 81. So (3,7,9) is NOT a Pythagorean Triple. (3,4,5): 3 to the power of 2 + 4 to the power of 2 =25 where as 5 to the power of 2 equals to 25. So, (3,4,5) is a Pythagorean Triple.

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Original Problems

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Bibliography (Resources) MYP 3 MATH BOOK FOR INTERNATIONAL IB STUDENTS (problems + explanations) http://www.redmond.k12.or.us/14552011718214563/lib/ 14552011718214563/Lesson_9.2.pdf (For the Converse of Pythagorean Theorem Problems) http://www.math.brown.edu/~jhs/frintch2ch3.pdf

Thursday, April 5, 2012