Download Pythagorean Theorm

1.
2.
3.
4.
5.
Leg – One of 2 sides of a right triangle
Hypotenuse – the longest side of a right triangle
Triangle- a 3-sided polygon
Polygon- a 2-D figure, has at least 3 sides
Equilateral- all sides equal
6. Isosceles- 2 sides are equal
7. Scalene- NO sides are equal
8. Pythagorean Theorem- a formula to find a side of a right
triangle ( a^2 + b^2 = c^2 )
9. Right Angle- a 90 degree angle
10. Right Triangle- a triangle with 2 legs, a hypotenuse, and
a right angle
11. Degrees- a measurement of an angle represented by a
small circle
12. Radians- a measurement of an angle represented by a
small hash mark (‘)
13. Side, Side, Side (SSS)- A method to prove that 2 or more
triangles are congruent by having 3 congruent sides
14. Angle, Side, Angle (ASA)- A method to prove that 2 or
more triangles are congruent by having an angle, a side,
and an adjoining angle congruent
15. Angle, Angle, Angle (AAA)- A method to prove that 2 or
more triangles are congruent by having 3 congruent angles
16. Congruent- equal
17. Similar- close, but not 100% congruent (usually a scale
drawing)
18. Parallel- are two lines that never cross
19. Perpendicular- are two lines that cross at a right
angle
20. Straight Angle- a 180 degree line
21. Complementary- two angles that add to 90
degrees
22. Supplementary – two angles that add to 180
degrees
23. Perimeter – How much distance is around an
object (Fence) (2-D)
24. Area – How much it takes to cover an object
(Carpet) (2-D)
25. Volume – How much it takes to fill an object (3D)
Pythagorean Theorem
c2 = a2 + b2
Perimeter
PolygonsP = add all sides
Area
Triangle A = (1/2)bh
Square/Rectangle A = bh
Trapezoid A = (1/2) (p + q)h
Volume
Prisms V = (BA)h
Cones V = (1/3)(BA)h
Cylinders
V = (BA)h
Sphere
V = (4/3)(BA)h
Hemisphere
V = (2/3)(BA)h
Shape
Picture
Sides
Perimeter
Area
Triangle
3
P=a+b+c
A = (1/2)bh
Square
4
P = 4s
A = bh
Rectangle
4
P = 2b + 2h
A = bh
Pentagon
5
Add all sides
----------------
Hexagon
6
Add all sides
----------------
Heptagon
7
Add all sides
----------------
Octagon
8
Add all sides
----------------
Nonagon
9
Add all sides
----------------
Decagon
10
Add all sides
----------------
Dodecagon
12
Add all sides
----------------
No Perimeter!
No Sides!
Circumference -------------- C = 2πr
C = dπ
Area ------------------------- A = πr2
• Traditional Formula: d = √(X2 – X1) + (Y2 – Y1)
• THERE MUST BE AN EASIER WAY!
1.
2.
3.
4.
Draw a triangle
Determine leg lengths
Solve for hypotenuse length
Draw a conclusion
-
Pg. 6 -10
Pg. 22
Pg. 35
Pg. 39
Pg. 37
The diagram is named for its creator, Theodorus of Cyrene (sy ree
nee), a former Greek colony. Theodorus was a Pythagorean.
The Wheel of Theodorus begins with a triangle with legs 1 unit
long and winds around counterclockwise. Each triangle is drawn
using the hypotenuse of the previous triangle as one leg and a
segment of length 1 unit long as the other leg. To make the Wheel
of Theodorus, you need only know how to draw right angles and
segments 1 unit long.
1.
2.
3.
4.
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6.
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9.
Objectives (2 minimum)
Hypothesis (3 minimum)
Materials
Procedure
Data (Chart, Graph, Equation)
Observations (3 minimum)
Calculations
Conclusion/Errors (4 sentence minimum)
Extension Problems
-Refer to the blue sheet
- Use your action words!
- Try to pick from the 3 columns
farthest to the right
- What are we trying to solve?
- What do you think?
- What will happen?
-What will you use to create this design?
- Not all designs are created the same!
- What are the steps to do this project?
- You can update it as you go if it does not
make sense.
Leg a
Triangle 1
Triangle 2
Triangle 3
Triangle 4
Triangle 5
Triangle 6
Triangle 7
Triangle 8
Triangle 9
Triangle 10
Triangle 11
Leg b
Hypotenuese
-What do you notice?
-What elements were hard?
-What elements were easy?
1.
2.
3.
4.
Make a table of all the triangles and the hypotenuse lengths.
Graph the data (computer or by hand)
Develop an equation if possible
Describe the data (Increasing/Decreasing? Growth/Decay?,
Constant?, etc…)
1.
2.
3.
4.
Were your hypothesis right or wrong? Why?
Did you have any errors? How did they effect your design?
What unit of measure did you use for your triangles?
Why did you choose to decorate your project the way you
did?
• For each hypotenuse length that is not a whole number:
Give the two consecutive whole numbers the length is
between. For example √2 is between 1 and 2.
• Odakota uses his calculator to find √3. He gets
1.732050808. Geeta says this must be wrong because
when she multiplies 1.732050808 by 1.732050808, she
gets 3.000000001. Why do these students disagree?
• Pg. 54 and 55
•Problems 8-10
Shape
Faces
Edges
Vertices
Volume
Triangular Prism 5
9
6
V = (BA)h
Square Prism
6
12
8
V = (BA)h
Rectangular
Prism
6
12
8
V = (BA)h
Trapezoidal
Prism
7
15
10
V = (BA)h
Cylinder
3
2
0
V = (BA)h
Cone
2
1
1
V = (1/3)(BA)h
Sphere
1
0
0
V = (4/3)(BA)h
Hemisphere
2
1
0
V = (2/3)(BA)h
•Pg. 60
•Problem 47 and 48