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# Converses and Inverses

Lesson 1 of 10

## Objective: SWBAT write the converse and inverse of a conditional statement and engage in mathematical practice discourse and precision standards

#### Do Now

*10 min*

As the students walk in the room, I hand them a page from the book *Alice’s Adventures in Wonderland* by Lewis Carroll to read:

During my unit on transformations, students used examples from *Alice...* to illustrate transformations. This time, I use the book to show students examples of logical reasoning. In addition to writing children’s books, Lewis Carroll was a mathematician who specialized in mathematical logic and examples of logical reasoning can be shown throughout the book.

#### Resources

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#### Mini-Lesson

*15 min*

To begin the Mini-Lesson, we discuss the definition of **logical reasoning**. Students are able to come up with a basic definition, but are often unaware that logic is a branch of mathematics. It is helpful to point out how logic relates to MP3 construct viable arguments and critique the reasoning of others. We also discuss how logic is needed to write formal proofs.

The next part of the Mini-Lesson is to go over descriptions of following terms:

- conditional statement
- hypothesis
- conclusion
- converse
- inverse

In mathematics these words have different meanings than in some other contexts where students might use them. For example, a scientific hypothesis is a different thing than a mathematical hypotheses. For many of my students, this is the first time using the words in math class. So, I take time here to discuss how the meanings shift between contexts. How are they similar? How do they differ?

Before I ask students work on their own, we will:

- Go over some examples of identifying the hypothesis and conclusions of conditional statements
- Write the converse and inverse of these conditional statements

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#### Summary

*5 min*

For today's Exit Ticket, I ask students to write the converse of the following statement:

**If two sides of a triangle are congruent, then the angles opposite from those sides are congruent.**

This introduces students to the **Isosceles Triangle Theorem** and its converse, which will be further investigated in a later lesson.

Students are given a homework sheet to practice writing more converses and inverses of conditional statements.

#### Resources

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- UNIT 1: Preparing for the Geometry Course
- UNIT 2: Geometric Constructions
- UNIT 3: Transformational Geometry
- UNIT 4: Rigid Motions
- UNIT 5: Fall Interim Assessment: Geometry Intro, Constructions and Rigid Motion
- UNIT 6: Introduction to Geometric Proofs
- UNIT 7: Proofs about Triangles
- UNIT 8: Common Core Geometry Midcourse Assessment
- UNIT 9: Proofs about Parallelograms
- UNIT 10: Similarity in Triangles
- UNIT 11: Geometric Trigonometry
- UNIT 12: The Third Dimension
- UNIT 13: Geometric Modeling
- UNIT 14: Final Assessment

- LESSON 1: Converses and Inverses
- LESSON 2: Contrapositives
- LESSON 3: Biconditionals
- LESSON 4: What are Geometric Proofs?
- LESSON 5: Algebraic Proofs
- LESSON 6: Proofs using Postulates
- LESSON 7: Proofs about Angles
- LESSON 8: Parallel Lines Intersected by a Transversal
- LESSON 9: Proofs about Perpendicular Bisectors
- LESSON 10: Introduction to Proofs Assessment