Given: the cost of two items is more than $50.

Slides:

Advertisements

Similar presentations

Using Indirect Reasoning

Advertisements

PROOF BY CONTRADICTION

Write the negation of “ABCD is not a convex polygon.”

Chapter 5: Relationships Within Triangles 5.4 Inverses, Contrapositives, and Indirect Reasoning.

5-4 Inverses, Contrapositives, and Indirect Reasoning

Introduction Isosceles triangles can be seen throughout our daily lives in structures, supports, architectural details, and even bicycle frames. Isosceles.

Anna Chang T2. Angle-Side Relationships in Triangles The side that is opposite to the smallest angle will be always the shortest side and the side that.

So far we have learned about:

Accelerated Math I Unit 2 Concept: Triangular Inequalities The Hinge Theorem.

4-3 A Right Angle Theorem Learner Objective: Students will apply a Right Angle Theorem as a way of proving that two angles are right angles and to solve.

Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

By: Sean Bonner and Tyler Martin.  Properties of Inequality  If a > b and c ≥ d, then a + c > b + d  If a > b and c > c then ac > bc and a/c > b/c.

5.6 Indirect Proof and Inequalities in Two triangles.

Day 6 agenda Return/go over quizzes- 10 min Warm-up- 10 min 5.4 Notes- 50 min 5.4 Practice- 15 min Start homework- 5 min.

Relationships within Triangles Chapter Midsegment Theorem and Coordinate Proof Midsegment of a Triangle- a segment that connects the midpoints.

Bell Work Conditional: If the car is running, then it has fuel 1) Write the converse 2) Write the “opposite” statement of the conditional 3) Write the.

Geometry 6.3 Indirect Proof.

Section 2.21 Indirect Proof: Uses Laws of Logic to Prove Conditional Statements True or False.

GEOMETRY 4-5 Using indirect reasoning Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz.

Logical Reasoning:Proof Prove the theorem using the basic axioms of algebra.

5-4 Inverses, Contrapositives, and Indirect Reasoning

Warm Up. Writing the negation of each statement. 1)The m

Chapter 6 Review. + DEFINITION OF INEQUALITY Difference in size, degree or congruence A B

5-5 Indirect Proof. Indirect Reasoning In indirect reasoning, all possibilities are considered and then all but one are proved false. – The remaining.

Geometry Mini Quiz 12/10/15 1) 3) Fill in the chart. Write the name of the point of concurrency (where they meet). 2) AltitudesAngle Bisector MediansPerpendicular.

Inverse, Contrapositive & indirect proofs Sections 6.2/6.3.

Method of proofs.  Consider the statements: “Humans have two eyes”  It implies the “universal quantification”  If a is a Human then a has two eyes.

5.1 Indirect Proof Objective: After studying this section, you will be able to write indirect proofs.

Friday, November 9, 2012 Agenda: TISK; No MM. Lesson 5-6: Compare side lengths and measures using the Hinge Theorem. Homework: 5-6 Worksheet.

Bellwork Write if-then form, converse, inverse, and contrapositive of given statement. 3x - 8 = 22 because x = 10.

5-5 Indirect Proof. Indirect Reasoning: all possibilities are considered and then all but one are proved false. The remaining possibility must be true.

5.5 Indirect Reasoning -Indirect Reasoning: All possibilities are considered and then all but one are proved false -Indirect proof: state an assumption.

 You will be able to use theorems and definitions to find the measures of angles.  You will be able to use theorems and definitions to write a formal.

EXAMPLE 3 Write an indirect proof Write an indirect proof that an odd number is not divisible by 4. GIVEN : x is an odd number. PROVE : x is not divisible.

5.6 Comparing Measures of a Triangle

5.1 Midsegments of Triangles

5-5 Inequalities in Triangles

3.1 Indirect Proof and Parallel Postulate

6.5 Inequalities in Triangles and Indirect Proofs

You will learn to use indirect reasoning to write proofs

5-4: Inverses, Contrapositives, and Indirect Reasoning

5.6 Indirect Proof and Inequalities in Two Triangles

Chapter 6: Inequalities in Geometry

Objectives Write indirect proofs. Apply inequalities in one triangle.

LESSON 5–4 Indirect Proof.

2.6 Prove Statements About Segments and Angles

Triangle Inequality Theorem

Check It Out! Example 1 Write an indirect proof that a triangle cannot have two right angles. Step 1 Identify the conjecture to be proven. Given: A triangle’s.

6.5 Indirect proof inequalities in one triangle

Lesson 5 – 4 Indirect Proof

An indirect proof uses a temporary assumption that

Lesson 5-3 Indirect Proof.

Lesson 5-4 The Triangle Inequality

Inequalities In Two Triangles

Indirect Proofs.

PROOF BY CONTRADICTION

Triangle Inequality Theorem

DRILL If A is (2, 5) and B is (-3, 8), show segment AB is parallel to segment CD if C is (-1, 4) and D is (-11, 10). What is the length of AB? Slope Formula.

Class Greeting.

Inequalities in Geometry

To Start: 10 Points Explain the difference between a Median of a triangle and an altitude of a triangle?

Vocabulary Indirect Proof

Learning Targets I will identify the first step in an indirect proof.

5.6 Inequalities in Two Triangles and Indirect Proof

Chapter 5 Parallel Lines and Related Figures

5.6 Indirect Proof and Inequalities in Two Triangles

5.1 Indirect Proof Let’s take a Given: Prove: Proof: Either or

Presentation transcript:

Given: the cost of two items is more than $50. Use indirect reasoning to prove: If Jacky spends more than $50 to buy two items at a bicycle shop, then at least one of the items costs more than $25. Given: the cost of two items is more than $50. Prove: At least one of the items costs more than $25. Begin by assuming that the opposite is true. That is assume that neither item costs more than $25.

Given: the cost of two items is more than $50. Use indirect reasoning to prove: If Jacky spends more than $50 to buy two items at a bicycle shop, then at least one of the items costs more than $25. Given: the cost of two items is more than $50. Prove: At least one of the items costs more than $25. Begin by assuming that the opposite is true. That is assume that neither item costs more than $25. This means that both items cost $25 or less. This means that the two items together cost $50 or less. This contradicts the given information that the amount spent is more than $50. So the assumption that neither items cost more than $25 must be incorrect.

Therefore, at least one of the items costs more than $25. Use indirect reasoning to prove: If Jacky spends more than $50 to buy two items at a bicycle shop, then at least one of the items costs more than $25. Therefore, at least one of the items costs more than $25. This means that both items cost $25 or less. This means that the two items together cost $50 or less. This contradicts the given information that the amount spent is more than $50. So the assumption that neither items cost more than $25 must be incorrect.

Writing an indirect proof Step-1: Assume that the opposite of what you want to prove is true. Step-2: Use logical reasoning to reach a contradiction to the earlier statement, such as the given information or a theorem. Then state that the assumption you made was false. Step-3: State that what you wanted to prove must be true

Write an indirect proof: Assume has more than one right angle. That is assume are both right angles.

Write an indirect proof: If are both right angles, then According to the Triangle Angle Sum Theorem,. By substitution: Solving leaves:

Write an indirect proof: If: , This means that there is no triangle LMN. Which contradicts the given statement. So the assumption that are both right angles must be false.