Download 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.
1.1 Patterns and Inductive
Reasoning
• Essential Question: What is inductive reasoning?
• New Vocabulary
• Inductive Reasoning
• Conjecture
• Counterexample
• Inductive Reasoning 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.
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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.
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1.
2.
3.
4.
5.
6.
17, 23, 29, 35, 41, . . .
1.01, 1.001, 1.0001, . . .
12, 14, 18, 24, 32, . . .
2, -4, 8, -16, 32, . . .
1, 2, 4, 7, 11, 16, . . .
32, 48, 56, 60, 62, 63, . . .
• Homework:
• page 6-7 (1-29) odd, (56-59) all
1.2 Isometric Drawings and Nets
EQ: 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 Nets
EQ: 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
7. Choose the nets that will fold to make a cube.
A.
B.
C.
D.
• 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 Definitions
EQ: Define basic geometric terms
• Warm Up:
• Solve for the variable
1. x – 1 = 15 – x
2. -4b + 5b – 8 = 7 – 2b
3. -2(6x + 1) = -4x – 34
4. -5 + 3(n-3) = -4n
5. 7(-5 + 4a) = 5a + 5(4a – 7)
6. 8(5k – 6) = 8 (3k – 6)
7. 2 + 5x – 6x = -4x – 1
8. -7x – 2x = 8 – 7x
1-3, 1-4 Geometric Definitions
EQ: 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:
• 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
Warm Up
• Simplify each absolute value expression
1. |-6|
2. |3.5|
3. |7-10|
4. |-4 -2|
5. |-2-(-4)|
6. |-3 + 12|
• Solve each equation
7. x + 2x – 6 = 6
8. 3x + 9 + 5x = 81
9. w – 2 = -4 + 7w
Postulates and Axioms
• A postulate or an axiom is an accepted statement of fact.
1-5 Measuring Segments
If GJ = 32, find the value of each of the following.
3x
1.x
2.GH
3.HJ
x + 16
If AC = 58, find the value of
each of the following.
9. x
10.AB
11.BC
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 Angles
EQ: How do you identify angle relationships
• Warm Up:
• Evaluate each expression for m - -3 and n = 7
1. (m – n)2
2. (n – m ) 2
3. m2 + n2
Evaluate each expression for a = 6 and b = -8
4. (a - b) 2
5. √(a2 + b2) the entire expression is under the square root
6. (a + b)/2
1-6 Measuring Angles
EQ: How do you identify angle relationships?
1-8 The Coordinate Plane
EQ: 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 Plane
EQ: 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=
𝑥2 − 𝑥1
2
+ 𝑦2 − 𝑦1
2
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.)
1. P(-4,-2) and Q (1,3)
What is the midpoint of the segment with given endpoints?
2. H (12,8) X(-6,4)
What is the other endpoint?
3. endpoint (2,6), midpoint (5,12)
1-9 Perimeter, Circumference and Area
EQ: 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
1. rectangle: b = 4 m, h = 2 cm
2. square: s = 3.5 in
3. circle: d = 9 cm
1-7 Basic Constructions
EQ: 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
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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