Proofs using Postulates

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Objective

SWBAT apply postulates to geometric proofs.

Big Idea

Students will explore the equality postulates used in geometric proofs.

Do Now

5 minutes

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.

Mini-Lesson

15 minutes

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. 

Activity

20 minutes

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. 

Summary

5 minutes

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.