##
* *Reflection: Intervention and Extension
Proofs using Postulates - Section 3: Activity

My students were able to complete the first two proofs, but had difficulty with the last two. In order to help them, I gave them some statements and asked them to write the reasons in the third proof. Then for the last proof, I gave the students some reasons and asked them to write the statements. Some of the students were able to complete the proofs without my scaffold; however, when I teach this lesson again, I will prepare two versions of the activity sheet. Some students will work on a sheet with more of the simple proofs that have the scaffolds and others will work on the current sheet.

*Intervention and Extension: Proofs using Postulates*

# Proofs using Postulates

Lesson 6 of 10

## Objective: SWBAT apply postulates to geometric proofs.

*45 minutes*

#### Do Now

*5 min*

The Proofs Using Postulates Do Now shows students pictures of geometric figures and asks them to complete mathematical statements by making a valid conclusion from the diagram. All of the given statements relate to the Partition Postulate, which students will explore further in today's lesson. After about four minutes, we go over the answers.

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#### Mini-Lesson

*15 min*

We begin today's Mini-Lesson Presentation with a look at three properties of equality:

- Reflexive Property
- Symmetric Property
- Transitive Property

After students write down these properties, we move on to the Partition Postulate, which states, “A whole is equal to the sum of its parts.” Linking back to the Do Now, we look at how the postulate applies to both line segments and angles. When I click on the boxes Segment Sum and Angle Sum, the students can see an example of how the postulate applies. We then look back at the examples from the Do Now and identify which postulate applies to them. It is important for students to know these postulates in order to understand and write proofs (**MP6**).

Next, we use the postulates to write a simple two-column proof. This example uses the Angle Sum Postulate and the Addition Postulate, which students explored in the previous lesson. Students start the proof by brainstorming what they know and the information they will need for the proof. Then they write the Statement side of the proof independently. We will complete the Reason column of the proof together.

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#### Activity

*20 min*

In the Proofs Using Postulates Activity students are given four simple proofs to write. They take the first few minutes to brainstorm the information needed for the proof and then write the proofs (**MP3**). I have students work with partners to discuss their process. Working together can help students make sense of the proofs by allowing them to bounce ideas off each other. Since students in my class are usually in groups, I give pairs of students two proofs to work on. Before the end of the activity section, pairs share their proofs with the rest of the group.

After about 15 minutes, we go over the proofs and correct any incorrect statements or arguments. The most common errors that my students make regard switching the Properties of Equality. We sometimes have to go back over the differences between these three properties.

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#### Summary

*5 min*

To sum up the lesson, I have the students use a new piece of paper in their notebook to write a list of the postulates they’ve learned so far. They will continue to add to this sheet each time they learn a new postulate or theorem. This gives students a list to refer back to with all of the postulates and theorems in one place.

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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