Download Geometry Level 2 Ms. Sheppard-Brick 617-596

Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Do Now 1
Name:
Date:
Do Now 1 – Patterns and Inductive Reasoning
Week 1 Packet Page 1
Geometry Level 2
Inductive Reasoning
Name:
Date:
Inductive Reasoning
Vocabulary:
Inductive Reasoning _____________________________________________
_____________________________________________________________
Conjecture _____________________________________________________
_____________________________________________________________
Counterexample _________________________________________________
_____________________________________________________________
Premise: a reason offered as support for another claim
As a class you will watch two clips from the show House. For each scene, identify the premises
and conjectures in the table below:
Premises
Conjecture
Scene
One
Scene
Two
Week 1 Packet Page 2
Geometry Level 2
Inductive Reasoning
Name:
Date:
Using Inductive Reasoning in Arithmetic
Directions: Use the pattern in the examples to complete the conjecture.
Counterexamples
Directions: Find a counterexample to show that the statement is false. Answer in a complete
sentence or draw a figure and explain why it is a counterexample.
3. If the quotient of two numbers is positive, then both numbers must be positive.
4. If a four-sided shape has two sides the same length, then it must be a rectangle.
5. If a four-sided shape has opposite sides that are the same length, then it must be a square.
Week 1 Packet Page 3
Geometry Level 2
Inductive Reasoning
Name:
Date:
Using Inductive Reasoning in Geometry
For each situation, complete the chart and use inductive reasoning to make a conjecture.
6. Martine drew concurrent lines (lines that all share exactly one point) and determined
how many regions they divided her paper into.
Figure
Number
of Lines
1
2
2
4
3
4
5
Number
of
Regions
Complete Martine’s conjecture. If you draw n concurrent lines, it will divide your paper into
__________ regions.
7. Geraldo measured the sum of the angles in regular polygons and made the following
chart.
Figure
Number of
Sides
Angle Sum
3
4
5
180°
360°
540°
6
7
Complete Geraldo’s conjectures:
a) To find the number of degrees in a polygon with one more side, _______________
____________________________________________________________
b) The sum of the angles in a regular polygon with n sides is ___________________
Week 1 Packet Page 4
Homework 1
Name:
Date:
Geometry Level 2
Homework 1 – Finding Patterns
Directions: For problems 1-6, use inductive reasoning to find the next two figures you expect in
the pattern. Draw the two next figures.
Directions: for problems 7 – 14, use inductive reasoning to find the next two numbers in the
pattern. List the next two numbers.
Directions: for problem 15, show your work and/or explain how you got your answer for each
part of the problem.
15. Clara started a business braiding hair before proms and dances. The table below shows the
amount of profit Clara earned after each person paid.
Client Number
Profit Earned
1
$- 5
2
$10
3
$25
4
$40
5
6
a. Predict the amount of profit Clara will have earned after 5 customers and 6 customers.
Show or explain how you got your answer.
b. Clara started out by buying a special comb and sanitizer for her hair business when she
started. Use the chart to determine what her start-up expenses were. Show or explain
how you got your answer.
c. Clara predicts that she will earn a total profit of $280 by the end of prom season. How
many customers must Clara have in order to make this amount of profit? Show or
explain how you got your answer.
Week 1 Packet Page 5
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Do Now 2
Name:
Date:
Do Now 2 – Conjectures and Counterexamples
Try some cases, then complete the conjecture.
1. The sum of any three odd numbers is ______________.
2. The difference between and integer and its opposite is _________________.
Show the conjecture is false by finding a counterexample.
3. Conjecture: If a positive fraction is multiplies by a positive integer, then the product is
greater than the fraction.
4. Conjecture: If all the sides of a figure are the same length, then the figure must be a
square.
Week 1 Packet Page 6
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Undefined Terms - Notes
Name:
Date:
Undefined Terms – Guided Notes
In geometry, there are three terms/figures that are considered “undefined” because they cannot
be explained based on other terms.
Definitions:
Point:
Description:
Naming Conventions:
Figure:
Example(s):
Line
Description:
Naming Conventions:
Figure:
Example(s):
Week 1 Packet Page 7
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Undefined Terms - Notes
Name:
Date:
Plane
Description:
Naming Conventions:
Figure:
Example(s):
All of the other terms that we use in geometry can be defined based on these terms. Here are a
few of the first ones.
Collinear
Defintion:
Naming Conventions:
Figure:
Example(s):
Week 1 Packet Page 8
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Undefined Terms - Notes
Name:
Date:
Coplanar Points
Definition:
Naming Conventions:
Figure:
Example(s):
Coplanar Lines
Definition:
Naming Conventions:
Figure:
Example(s):
Week 1 Packet Page 9
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Undefined Terms - Notes
Name:
Date:
Examples:
Week 1 Packet Page 10
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Undefined Terms - Notes
Name:
Date:
Modeling Collinear Points and Coplanar Points and Lines
Your teacher will give you and your partner a few sticky notes to make points with. Place the
“points” somewhere visible within the classroom.
After all the points have been placed, walk around the room and answer the following questions.
1. Points _______, _________, and __________ are collinear because
______________________________________________________.
2. Points _______, _________, and __________ are not collinear because
_______________________________________________________.
3. Points _______, _________, __________ and __________ are not coplanar
because __________________________________________________.
4. Points _______, _________, ___________ and __________ are coplanar
because __________________________________________________.
5. Lines _________, ___________, and __________ are coplanar because
_______________________________________________________.
6. Lines _________, ___________, and __________ are not coplanar because
________________________________________________________.
Week 1 Packet Page 11
Geometry Level 2
Homework 3
Name:
Date:
Homework 3 – Points, Lines and Planes
Directions: Copy and complete each sentence. Include the answer in your answer column.
Directions: Name each of the figures described. Be sure to include the correct symbols.
Directions: In exercises 10 – 12, sketch and label each figure.
10. Sketch 𝐸𝐹 11. Sketch 𝐺𝐻 12. Sketch 𝐽𝐾 Directions: In exercises 13 – 14, a) name three points that are collinear and b) name three points that are not collinear. Directions: for problem 16, show your work and/or explain how you got your answer for each
part of the problem.
16. Danny sketched a figure that included points A, B, C, D, and E. In Danny’s figure, no three
points were collinear.
a. Sketch a figure that could be Danny’s figure.
b. Name each of the lines that are formed by the pairs of points in Danny’s figure.
c. Explain how you know that you named all of the possible lines in your answer to part b. Week 1 Packet Page 12
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Do Now 3
Name:
Date:
Do Now 3 – Points, Lines, and Planes
Directions: the figure at right to answer questions 9 – 13. 9. Name the points on plane S.
10. Name two lines.
11. Name the plane that contains point D.
12. Name three collinear points.
Week 1 Packet Page 13
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Chapter 1 Quiz 1 Review
Name:
Date:
Chapter 1 Quiz 1 Review Classwork
Students will be able to (SWBAT):
•
•
•
Find patterns and use them to make predictions.
Use inductive reasoning to make conjectures.
Use undefined terms and defined terms to describe figures.
Content Review:
Week 1 Packet Page 14
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Chapter 1 Quiz 1 Review
Name:
Date:
Quiz Practice:
Directions: Write or draw the next two terms in each sequence.
1.
2.
3.
4.
Directions: Show that each conjecture is false by drawing a counterexample.
5. If three lines lie in the same plane, then they intersect in at least one point.
6. Points A, G, and N are collinear. If AG = 7 inches and GN = 5 inches, then AN = 12 inches.
Week 1 Packet Page 15
Geometry Level 2
Ms. Sheppard-Brick
617-596-4133
Chapter 1 Quiz 1 Review
Name:
Date:
Directions: Use the diagram at right to answer the following questions.
7. Name three collinear points
8. Name three non-collinear points
Possible answer
D
9. Name four coplanar points
10. Name four non-coplanar points
Sample a
, B, and D Sample answer: J, D, P, and B
11. Name a line that intersects 𝐶𝐷.
12. Name the intersection of 𝐽𝐾and plane ℛ.
Directions: for problem 13, show your work and/or explain how you got your answer for each
part of the problem.
13. Amari drew the figures below on paper. Jenisteen measured each angle with a protractor.
They added the measures of each pair of angles to form a conjecture.
49°
131°
87°
93°
105°
75°
a. Complete the conjecture that they wrote “If two adjacent angles form a line, …”
b. Amari then drew one more figure. Jenisteen measured only one of the angles. Use your
conjecture to find the measure of the other angle. Show or explain how you got your answer.
115°
Week 1 Packet Page 16
Geometry Level 2
Homework 4
Name:
Date:
Homework 4 – Review For Chapter 1 Quiz 1
THIS IS A TWO PAGE ASSIGNMENT
Directions: Use inductive reasoning to find the next two numbers in each pattern. (TB 1.1)
1)
2)
3)
4)
! ! ! !
1, 10, 100, 1000, ?, ?
7, 3, -1, -5, -9, -13, ?, ?
1, 1, 2, 3, 5, 8, 13, ?, ?
32, 30, 26, 20, 12, ?, ?
5) , , , , ?, ?
! ! ! !
6) 1, 3, 6, 10, 15, 21, ? , ?
7) 1, 4, 9, 16, 25, 36, ? , ?
8) 1, 2, 4, 8, 16, 32, ? , ?
Directions: Use inductive reasoning to draw the next figure in each pattern. (TB 1.1)
9)
10)
Directions: Use the examples to complete the conjecture. (TB 1.2)
11) Conjecture: The product of 5 and any even
number is divisible by __?___.
Examples:
12) Conjecture: The square of an even number
is __?__.
Examples:
Directions: Give a counterexample in words, numbers, or a sketch to disprove each conjecture. (TB 1.2)
13) Conjecture: The difference of any two even numbers is positive.
14) Conjecture: If two circles touch each other, then one circle is inside the other circle.
Directions: Use the diagram at right for problems 15 – 20
15) Name three points that are collinear.
16) Name four points that are coplanar.
17) Name two lines that are coplanar.
18) Name three points that are not collinear.
19) Name four points that are not coplanar.
20) Name two lines that are not coplanar.
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Week 1 Packet Page 17
Geometry Level 2
Homework 4
Name:
Date:
Directions: for problems 21 and 22, show your work and/or explain how you got your answer for each
part of the problem.
21) Olivia makes the following conjecture: “The square of a number is greater than the number.”
a) Give two examples that support Olivia’s conjecture.
b) Sam believes that the conjecture is false. He points out that 1! = 1, and 1≯ 1 (1 is not greater
than 1). Find another counterexample to Olivia’s conjecture.
c) Rewrite the conjecture to make it true.
22) The table below shows figures composed of circles. The number of circles in each figure and the
diameter of each circle in each figure follow a pattern, as shown.
a. What is the number of circles in figure 5? Show or explain how you got your answer.
b. What is the diameter, in inches, of each circle in figure 5? Show or explain how you got your
answer.
c. What is the ratio of the number of circles in figure 6 to the number of circles in figure 7? Show or
explain how you got your answer.
d. Write an algebraic expression that could be used to determine the number of circles in figure n.
e. Write an algebraic expression that could be used to determine the diameter, in inches, of each
circle in figure n.
Week 1 Packet Page 18