welcome to hjh
TRANSCRIPT
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
BELL WORK
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Assumption High School
Geometry2016 – 2017
Day 18Topic: 2-5 to 2-6
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Chapter 2 Big Ideas
• Reasoning and Proof
• Essential Question• How can you make a conjecture and prove that it is true?
• In this chapter, you will:• Observe patterns leading to making conjectures.
• Solve equations giving reasons for each step and connect them to simple proofs.
• Prove geometric relationships using given information, definitions, properties, postulates, and theorems.
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Chapter 2 Essential Understanding
• 2-1 Patterns in some number sequences and some sequences of geometric figures can be used to discover relationships.
• 2-2 Some mathematical relationships can be described using a variety of if-then statements.
• 2-3 A definition is good if it can be written as a biconditional.
• 2-4 Given the true statements, deductive reasoning can be used to make a valid or true conclusion.
• 2-5 Algebraic properties of equality are used in geometry to solve problems and justify reasoning.
• 2-6 Given information, definitions, properties, postulates, and previously proven theorems can be used as reasons in a proof.
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Common Core State StandardsGeometry (GM)
• Use coordinates to prove simple geometric theorems algebraically.• GM: G-CO.C.9: Prove and apply theorems about lines and angles. Theorems
include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Student Objectives (2-1, 2-2 ,& 2-3)
• I can use inductive reasoning to make conjectures. (2-1)
• I can recognize conditional statements and their parts. (2-2)
• I can write converses, inverses, and contrapositives of conditionals. (2-2)
• I can write biconditionals and recognize good definitions. (2-3)
• I can connect reasoning in Algebra and Geometry. (2-5)
• I can prove and apply theorems about angles. (2-6)
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Properties of Equality & Congruence
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Properties
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Theorems
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Equality vs Congruence
• Equality is used for the measure of angles, and line segments without the line segment has mark above the letters.
• Congruence is used for angles and line segments with the hash mark on top.
• For example:
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Proof (Paragraph Proof)
• Mathematicians are often given the task to prove something is true.
• Proofs can be written initially in paragraph form and later demonstrated to be true using two-column proof form.
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Two-Column Proof
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Proving Angles Congruent
• Key Concepts• Theorem
• Paragraph Proof
• Theorem 2-1 Vertical Angles Theorem (p120)
• Theorem 2-2 Congruent Supplements Theorem (p122)
• Theorem 2-3 Congruent Complements Theorem (p123)
• Theorem 2-4 (p123) (Right angle congruence)
• Theorem 2-5 (p123) (Congruent & supplementary right angles)
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Chapter 2-6
• Turn in your books to page 120.
• We will review section 2-6 Key Terms and Problem Set (1-3) together.
• Follow along in your book so that you can write your notes more efficiently.
• Upon completion, you will complete the Lesson Check before you begin working on your worksheets 2-1 to 2-6.
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Chapter 2-6
• We will begin working on the Problem Set (1-3) in section 2-6 together.
• Upon completion of the example problem Got Its, you will be given 8 minutes to complete the Lesson Check on p.123
• We will review the Lesson check together before working on your worksheets.
• You will work on your worksheet packets until we have 30 minutes remaining in class when we will begin our review for tomorrow’s retest.
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Independent Practice
• You will now work on the worksheet packets 2-5 to 2-6 you were given yesterday.
• You will be given up to 25 minutes to work on these.
• You may work with a partner if you agree to do so quietly.
• Upon completion of the 25 minutes, we will review your work together and I will answer any questions you may have at that time.
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Review Starts Here
• Midpoint Formulas
• Distance Formula
• Pythagorean Theorem
• Perimeter
• Circumference
• Area
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Midpoint Formulas
• On a number line• The coordinate of the
midpoint is the average or mean of the the coordinates of the endpoints
• In the Coordinate Plane• The coordinates of the
midpoint are the average of the x-coordinates and the average of the y-coordinates of the endpoints.
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Distance Formula
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Pythagorean Theorem
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Perimeter
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Area
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
To be continued…
• Tomorrow we will retest on sections 1-7 to 1-8 Midpoint, Distance, Area, Circumference, & Perimeter.
• Homework: Study Study Study
• Your next test (1.3) on Chapter 2-1 through 2-6 will be Tuesday 02/07/2017.
• Visit our website for resources to help prepare you for your test.
http://fordmathletes.weebly.com/
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
We are a TEAM
• Remember what it mean to be part of a team…
•Together
•Everyone
•Achieves
•More
Mr. Matthew J Ford
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Following rules means being HAPPY
• Being HAPPY means being:
• Honest
• Accountable
• Proactive
• Positive
• Yourself
Mr. Matthew J Ford
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
Any Questions???
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Academic institution promoting High expectations resulting in Successful students
Assumption High School
You guy Rock!!!
•I Love all you crazy kiddos…
•You guys are real Mathletes in Training!