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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.

- 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

You have 5 minutes to play with your isometric paper.

Please leave plenty of room for work.

- 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

- 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

- 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:
- 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

- 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

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

- 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

- 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

You describe a point by an ordered pair (x,y) called the coordinates of the point.

- 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 =

- 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.

- 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

- 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)

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

- 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.

- 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