2. 1.Leg – One of 2 sides of a right triangle 2.Hypotenuse – the longest side of a right triangle 3.Triangle-a 3-sided polygon 4.Polygon-a 2-D figure, has at least 3 sides 5.Equilateral- all sides equal

3. 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

4. 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

5. 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

6. 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 (3- D)

7. Pythagorean Theoremc 2 = a 2 + b 2 Perimeter Polygons-P = 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 CylindersV = (BA)h SphereV = (4/3)(BA)h HemisphereV = (2/3)(BA)h

8. ShapePictureSidesPerimeterArea Triangle3P = a + b + cA = (1/2)bh Square4P = 4sA = bh Rectangle4P = 2b + 2hA = bh Pentagon5Add all sides---------------- Hexagon6Add all sides---------------- Heptagon7Add all sides---------------- Octagon8Add all sides---------------- Nonagon9Add all sides---------------- Decagon10Add all sides---------------- Dodecagon12Add all sides----------------

9. No Perimeter! No Sides! Circumference -------------- C = 2 π r C = d π Area ------------------------- A = π r 2

10. Traditional Formula: d = √(X 2 – X 1 ) + (Y 2 – Y 1 ) THERE MUST BE AN EASIER WAY!

11. 1.Draw a triangle 2.Determine leg lengths 3.Solve for hypotenuse length 4.Draw a conclusion

12. -Pg. 6 -10 -Pg. 22 -Pg. 35 -Pg. 39

13. Pg. 37

14. 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.

15. 1.Objectives (2 minimum) 2.Hypothesis (3 minimum) 3.Materials 4.Procedure 5.Data (Chart, Graph, Equation) 6.Observations (3 minimum) 7.Calculations 8.Conclusion/Errors (4 sentence minimum) 9.Extension Problems

16. -Refer to the blue sheet -Use your action words! -Try to pick from the 3 columns farthest to the right

17. -What are we trying to solve? -What do you think? -What will happen?

18. -What will you use to create this design? - Not all designs are created the same!

19. -What are the steps to do this project? -You can update it as you go if it does not make sense.

20. Leg aLeg bHypotenuese Triangle 1 Triangle 2 Triangle 3 Triangle 4 Triangle 5 Triangle 6 Triangle 7 Triangle 8 Triangle 9 Triangle 10 Triangle 11

21. -What do you notice? -What elements were hard? -What elements were easy?

22. 1.Make a table of all the triangles and the hypotenuse lengths. 2.Graph the data (computer or by hand) 3.Develop an equation if possible 4.Describe the data (Increasing/Decreasing? Growth/Decay?, Constant?, etc…)

23. 1.Were your hypothesis right or wrong? Why? 2.Did you have any errors? How did they effect your design? 3.What unit of measure did you use for your triangles? 4.Why did you choose to decorate your project the way you did?

24. 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?

25. Pg. 54 and 55 Problems 8-10

26. ShapeFacesEdgesVerticesVolume Triangular Prism596V = (BA)h Square Prism6128V = (BA)h Rectangular Prism 6128V = (BA)h Trapezoidal Prism 71510V = (BA)h Cylinder320V = (BA)h Cone211V = (1/3)(BA)h Sphere100V = (4/3)(BA)h Hemisphere210V = (2/3)(BA)h

27. Pg. 60 Problem 47 and 48