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Tools of Geometry - PowerPoint PPT Presentation

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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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.

1.1 Patterns and Inductive Reasoning

• Essential Question: What is inductive reasoning?

• New Vocabulary

• Inductive Reasoning

• Conjecture

• Counterexample

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

• 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.

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

• 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.

• 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, . . .

• Homework:

• page 6-7 (1-29) odd, (56-59) all

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.

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

• 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

• 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

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

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.

• Definition foldable:

• 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

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

Postulates and Axioms

• A postulate or an axiom is an accepted statement of fact.

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.

• Angles with the same measure are congruent angles.

• Relationships between angles worksheet activity

• Homework:

• p 33 (1-15) odd

• p 40 (1-33) odd

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

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.

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 =

The Midpoint Formula

• You can find the coordinates of the midpoint of a segment by averaging the x coordinates and averaging the y coordinates of the endpoints.

• QS has endpoints Q(3,5) and S (7, -9). Find the coordinates of the midpoint.

• AB has endpoints A (8,9) and B (-6,-3). Find the coordinates of the midpoint.

• The midpoint of AB is M(3,4). One endpoint is A (-3, -2). Find the coordinates of the other endpoint.

• The midpoint of XY is M(4,-6). One endpoint is X (2, -3). Find the coordinates of Y.

• Complete distance and midpoint worksheet.

• When finished hand it in to me to check. Then begin working on your construction that you are going to teach.

1-7 Basic Constructions

• Each student will be assigned a construction to master at home. Next week you will be responsible to teach your group how to complete the construction. Remember that constructions are completed using only a straight edge and a compass!

• Please write down which construction you need to learn. All instructions are in your textbook in section 1-7.

• Homework: Due Monday

• Have practiced your construction to the point that you can teach the other members of your table group to complete it.

• page 56 (1-31) odd

Warm Up:

• What is the distance between the points: (If you don’t have a calculator leave as an unsimplified radical.)

• P(-4,-2) and Q (1,3)

What is the midpoint of the segment with given endpoints?

• H (12,8) X(-6,4)

What is the other endpoint?

3.endpoint (2,6), midpoint (5,12)

1-9 Perimeter, Circumference and AreaEQ: How do you find perimeter and area of basic shapes?

• Glue your formula chart into your notebook. Label the shapes then fill in the formulas for perimeter and area.

1-9 Perimeter, Circumference and Area

• The units for perimeter or circumference are inches, feet, meters, etc

• The units for area are square feet, square inches etc.

• Find the perimeter of this triangle.

• Please take out the homework from yesterday and today

• page 56 (1-31) odd

• page 65 (1-37) odd

• Warm Up:

• Find the area of each figure to the nearest hundredth

• rectangle: b = 4 m, h = 2 cm

• square: s = 3.5 in

• circle: d = 9 cm

1-7 Basic ConstructionsEQ: How do you make basic constructions using only a straightedge and a compass?

• In a construction you use a straightedge and a compass to draw a geometric figure.

• A straightedge is a ruler with no markings on it.

• A compass is a geometric tool used to draw circles and parts of circles called arcs.

1-7 Basic Constructions

• You will learn four constructions

• Congruent Segments

• Congruent Angles

• Perpendicular Bisector

• Angle Bisector

• Perpendicular lines are lines that intersect to form right angles. The symbol  means “Is perpendicular to”

• A bisector divides something into equal parts.

• Take turns demonstrating and explaining the construction you were assigned. Once you have practiced a construction, complete that construction on the handout.

• Write the steps for each construction in your notebook.

• The compass marks show that you are making a construction, not just measuring!

• If you do not have someone at your table for one of the constructions, find someone from another group to demonstrate it for you.

• When your whole group is finished, pick up the Ch 1 Vocabulary Review worksheet.

• Test on Chapter 1 – next class meeting.

• Complete Vocabulary review worksheet

• Complete review problems in textbook

• page 72: 27-31, 34-44 all