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Tools of Geometry

Tools of Geometry . Chapter 1. Please place your signed syllabus and textbook card in the basket on the table by the door. Take out your group’s work on the watermelon problem. Have one person in your group get a large sheet of white paper off the table by the door.

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Tools of Geometry

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  1. Tools of Geometry Chapter 1

  2. Please place your signed syllabus and textbook card in the basket on the table by the door. • Take out your group’s work on the watermelon problem. • Have one person in your group get a large sheet of white paper off the table by the door.

  3. 1.1 Patterns and Inductive Reasoning • Essential Question: What is inductive reasoning? • New Vocabulary • Inductive Reasoning • Conjecture • Counterexample

  4. InductiveReasoning is reasoning that is based on patterns you observe.

  5. 384, 192, 96, 48,… • Make up a number pattern and exchange it with the person sitting next to you. See if you can determine the next two numbers in the sequence.

  6. A conjecture is a conclusion you reach using inductive reasoning.

  7. A counterexample to a conjecture is an example for which is conjecture is incorrect. • You can prove a conjecture is false by finding one counterexample. • Find a counterexample: • The square of any number is greater than the original number. • You can connect any three points to form a triangle. • Any number and its absolute value are opposites. • If a number is divisible by 5 then it is also divisible by 10.

  8. 1. 17, 23, 29, 35, 41, . . . • 2. 1.01, 1.001, 1.0001, . . . • 3. 12, 14, 18, 24, 32, . . . • 4. 2, -4, 8, -16, 32, . . . • 5. 1, 2, 4, 7, 11, 16, . . . • 6. 32, 48, 56, 60, 62, 63, . . .

  9. Homework: • page 6-7 (1-29) odd, (56-59) all

  10. 1.2 Isometric Drawings and NetsEQ: How do you make a three dimensional drawing? You have 5 minutes to play with your isometric paper. Please leave plenty of room for work.

  11. 1.2 Isometric Drawings and NetsEQ: How do you make a three dimensional drawing?

  12. Using the isometric cubes build a three dimensional shape that can stand on its own. Use at least 10 cubes • Draw the structure you built on the isometric paper. • Draw an orthographic sketch of the structure • Draw a foundation drawing of the structure

  13. Exit Pass: Explain the difference between an isometric drawing, an orthographic drawing and a foundation drawing. Draw a foundation drawing for this shape: • Put the exit pass in the geometry basket on your way out the door. (or when you finish) • Homework: p13 (1-20) all

  14. 1-3, 1-4 Geometric DefinitionsEQ: Define basic geometric terms • Warm Up: • Solve for the variable • x – 1 = 15 – x • -4b + 5b – 8 = 7 – 2b • -2(6x + 1) = -4x – 34 • -5 + 3(n-3) = -4n • 7(-5 + 4a) = 5a + 5(4a – 7) • 8(5k – 6) = 8 (3k – 6) • 2 + 5x – 6x = -4x – 1 • -7x – 2x = 8 – 7x

  15. 1-3, 1-4 Geometric DefinitionsEQ: Define basic geometric terms • Definition Posters • Draw a word out of the selections • You must create a poster for the term. The poster must include a good definition and a drawing that represents the term. • Make it clear and easy to read.

  16. Definition foldable: • PLEASE read instructions carefully before you do ANYTHING!! • Fold your paper along the VERTICAL lines and then unfold. • Using scissors, carefully cut ONLY along the dashed lines. • Glue the chart onto a piece of binder paper or into your notebook, so when you fold the tabs in you can read the words and you have blank spaces inside the chart. • On the inside of each tab, write the definition of the term, and then draw a drawing of the term. • Move around the room until you have filled in all the definitions

  17. Warm Up • Simplify each absolute value expression • |-6| • |3.5| • |7-10| • |-4 -2| • |-2-(-4)| • |-3 + 12| • Solve each equation • x + 2x – 6 = 6 • 3x + 9 + 5x = 81 • w – 2 = -4 + 7w

  18. Postulates and Axioms • A postulate or an axiom is an accepted statement of fact.

  19. 1-5 Measuring Segments

  20. 1-6 Measuring Angles • Angles are formed by two rays with a common endpoint. • The rays are the sides of the angle. • The endpoint is its vertex.

  21. Angles with the same measure are congruent angles. • Relationships between angles worksheet activity

  22. Homework: • p 33 (1-15) odd • p 40 (1-33) odd

  23. 1-6 Measuring AnglesEQ: How do you identify angle relationships • Warm Up: • Evaluate each expression for m - -3 and n = 7 • (m – n)2 • (n – m ) 2 • m2 + n2 Evaluate each expression for a = 6 and b = -8 • (a - b) 2 • √(a2 + b2) the entire expression is under the square root • (a + b)/2

  24. 1-6 Measuring AnglesEQ: How do you identify angle relationships?

  25. 1-8 The Coordinate PlaneEQ: How do you find the distance between two points? You describe a point by an ordered pair (x,y) called the coordinates of the point.

  26. 1-8 The Coordinate PlaneEQ: How do you find the distance between two points? • To find the distance between two points that are not on a horizontal or vertical line, you can use the distance formula. • Find the distance between R (5,2) and T (-4, -1) • let (5,2) be (x1, y1) and (-4, -1) be (x2, y2) • d =

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