Use algebra to write two-column proofs.

Slides:

Advertisements

Similar presentations

Advertisements

6.2 Parallelograms.

2-6 Algebraic Proof p. 136 You used postulates about points, lines, and planes to write paragraph proofs. Use algebra to write two-column proofs. Use properties.

Over Lesson 2–5 5-Minute Check 1 In the figure shown, A, C, and lie in plane R, and B is on. Which option states the postulate that can be used to show.

Vocabulary algebraic proof – Made up of algebraic statements two-column proof/formal proof – contains statements and reasons in two columns.

Lesson 2 – 6 Algebraic Proof

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) CCSS Then/Now New Vocabulary Postulates: Points, Lines, and Planes Key Concept: Intersections.

UNIT 01 – LESSON 11 – ALGEBRAIC PROOFS ESSENTIAL QUESTION How can algebraic properties help you solve an equation? SCHOLARS WILL… Use algebra to write.

Lesson: 15 – 4 Preparing for Two-Column Proofs

Warm Up. Warm Up Answers Theorem and Proof A theorem is a statement or conjecture that has been shown to be true. A theorem is a statement or conjecture.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–6) CCSS Then/Now Postulate 2.8: Ruler Postulate Postulate 2.9: Segment Addition Postulate.

Geometry, Quarter 2, Unit 2.3 Proving Theorems About Parallelograms Days: 11.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–5) CCSS Then/Now New Vocabulary Key Concept: Properties of Real Numbers Example 1:Justify.

Splash Screen. CCSS Content Standards G.CO.11 Prove theorems about parallelograms. G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.

2.5 Reasoning in Algebra and Geometry Algebraic properties of equality are used in Geometry. –Will help you solve problems and justify each step. In Geometry,

Algebraic Proof LESSON 2–6. Lesson Menu Five-Minute Check (over Lesson 2–5) TEKS Then/Now New Vocabulary Key Concept: Properties of Real Numbers Example.

2.5 Reasoning and Algebra. Addition Property If A = B then A + C = B + C.

USING PROPERTIES FROM ALGEBRA ALGEBRAIC PROPERTIES OF EQUALITY Let a, b, and c be real numbers. SUBTRACTION PROPERTY ADDITION PROPERTY If a = b, then a.

Geometry Organising is what you do before you do something, so that when you do it, it is not all mixed up. A.A. Milne Today: Over Proof Intro 2.5.

A. A line contains at least two points.

2.5 Algebraic Proof Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction.

Geometry I've got a theory that if you give 100 percent all of the time, somehow things will work out in the end. Larry Bird Today: Homework Check 3.5.

Chapter 2.6 Algebraic Proof.

Five-Minute Check (over Lesson 2–4) Mathematical Practices Then/Now

Unit 1 Day 10 TWO COLUMN PROOFS.

1. SWBAT use algebra to write two column proofs

SWBAT write 2-column proofs

Use the SSS Postulate to test for triangle congruence.

Use the ASA Postulate to test for congruence.

Write proofs involving supplementary and complementary angles.

Starter(s): Find one counterexample to show that each conjecture is false. All vehicles on the highway have exactly four wheels. 2. All states in the United.

Identify and use basic postulates about points, lines, and planes.

Find the measure of each numbered angle and name the theorem that justifies your work. Problem of the Day.

If an organism is a parasite, then it survives by living on or in a host organism. If a parasite lives in or on a host organism, then it harms its.

Calculate with measures.

KP ≅ PM PM ≅ NM KP ≅ NM ∠KLP ≅ ∠MLN ∠KLP ≅ ∠PLN ∠PLN ≅ ∠MLN

Geometry/Trig Name __________________________

2-5, 6, & 7 Geometric Proofs.

LESSON 2–6 Algebraic Proof.

Objectives Write two-column proofs.

Five-Minute Check (over Lesson 5–3) Mathematical Practices Then/Now

2-6 Algebraic Proof Use algebra to write two-column proofs.

Prove Statements about Segments and Angles

Section 2.4 Algebraic Reasoning

Find the value of the variable and the measure of each angle.

Five-Minute Check (over Lesson 2–6) Mathematical Practices Then/Now

Five-Minute Check (over Lesson 2–4) Mathematical Practices Then/Now

Mathematical Practices

Five-Minute Check (over Lesson 2–3) Mathematical Practices Then/Now

Proving Statements about Segments

Presentation transcript:

Use algebra to write two-column proofs. Use properties of equality to write geometric proofs. Splash Screen

Preparation for G.CO.9 Prove theorems about lines and angles. Content Standards Preparation for G.CO.9 Prove theorems about lines and angles. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. CCSS

algebraic proof two-column proof formal proof Vocabulary

Vocabulary

Concept

Justify Each Step When Solving an Equation Solve 2(5 – 3a) – 4(a + 7) = 92. Example 1

Solve –3(a + 3) + 5(3 – a) = –50. Example 1

Write an Algebraic Proof Example 2

Write an Algebraic Proof Statements Reasons Proof: Example 2

Which of the following statements would complete the proof of this conjecture? If the formula for the area of a trapezoid is , then the height h of the trapezoid is given by . Example 2

Statements Reasons Proof: Example 2

Write a Geometric Proof If A B, mB = 2mC, and mC = 45, then mA = 90. Write a two-column proof to verify this conjecture. Example 3

Write a Geometric Proof Statements Reasons Proof: Example 3

Example 3

3. Definition of congruent segments Statements Reasons Proof: 1. Given 1. 2. 2. _______________ ? 3. AB = RS 3. Definition of congruent segments 4. AB = 12 4. Given 5. RS = 12 5. Substitution Example 3

Homework Page 139 (9-20) Vocabulary