3.4+Measuring+the+Egyptian+Way

toc Oct 27 08 ESK =3.4 Measuring the Egyptian Way=

A. 1. Do the whole-number lengths 3, 4, and 5 satisfy the relationship a2+b2=c2?
3x3 + 4x4 = 5x5 = 9 + 16 = 25 Therefore, yes, the whole number 3,4, and 5 satisfy the relationship a2+b2=c2.

2. **Form a triangle using string or straws cut to these lengths.**
a picture will be updated..........................................................

3. **Is the triangle you formed a right triangle?**
Yes, the triangle that I formed is a right triangle, and can prove by Pythagorean theorem.

4. **Repeat parts 1-3 with the lengths 5, 12, and 13.**
5x5 + 12x12 = 13x13 = 25 + 144 = 169 There fore, yes, the who number 5,12, and 13 satisfy the relationship a2+b2=c2. a picture will be updated......................................................... Yes, the triangle that I formed is a right triangle, and can prove by Pythagorean theorem.

B. **1. Form a triangle with side lengths a,b, and c that do not satisfy the relationship a2+b2=c2**
1x1 + 2x2 =\ 3x3 1 + 4 =\ 9 ( =\ means not equal)

** 2. Is the triangle a right trianlgle? **
No, this triangle is not a right triangle, but it is a obtuse triangle.

3. Repeat parts 1 and 2 with a different triangle.
4x4 + 6x6 =/ 7x7 =\ 16 + 36 =\ 49 No, this triangle is not a right triangle but it is a acute triangle.

4. Make a conjecture about triangles whose side lengths do not satisfy the relationship a2+b2=c2.
If a2+b2 bigger than c2, the triangle is acute triangle. If it satisfy the relationship, a2+b2 less than c2, the triangle is obtuse triangle. This shows exactly in question B.

1. Determine whether the triangle with the given side lengths is a right triangle.
A. 12,16,20 12,16 and 20 would be a right triangle, because it is the ratio of 3,4 and 5. B. 8,15,17 8,15,17 is a right triangle, because it satisfy the Pythagorean Theorem. C. 12,9,16 12, 9, and 16 is NOT a right triangle, becasuse it doesn't satisfy the Pythagorean Theorem.