Transcript
Academic institution promoting High expectations resulting in Successful students
Assumption High School
BELL WORK
Academic institution promoting High expectations resulting in Successful students
Assumption High School
Assumption High School
Geometry2016 – 2017
Day 18Topic: 2-5 to 2-6
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.
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.
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.
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)
Academic institution promoting High expectations resulting in Successful students
Assumption High School
Properties of Equality & Congruence
Academic institution promoting High expectations resulting in Successful students
Assumption High School
Properties
Academic institution promoting High expectations resulting in Successful students
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Theorems
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:
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.
Academic institution promoting High expectations resulting in Successful students
Assumption High School
Two-Column Proof
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)
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.
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.
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.
Academic institution promoting High expectations resulting in Successful students
Assumption High School
Review Starts Here
• Midpoint Formulas
• Distance Formula
• Pythagorean Theorem
• Perimeter
• Circumference
• Area
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.
Academic institution promoting High expectations resulting in Successful students
Assumption High School
Distance Formula
Academic institution promoting High expectations resulting in Successful students
Assumption High School
Pythagorean Theorem
Academic institution promoting High expectations resulting in Successful students
Assumption High School
Perimeter
Academic institution promoting High expectations resulting in Successful students
Assumption High School
Area
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/
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
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
Academic institution promoting High expectations resulting in Successful students
Assumption High School
Any Questions???
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!
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