The introductory unit in my high school geometry course is dedicated to lines and angles. These are often referred to as the building blocks of geometry. The topics in this unit are essential understandings for geometry students that are needed to build knowledge throughout the course. Since this unit is so important, we mostly add new pages to our interactive notebooks. Read on to see our geometry interactive notebook pages for lines and angles, and how this unit develops.
For our first day of content, we cover algebraic proof. This way we can review equation solving, and simultaneously learn about proofs. We actually do this lesson before students even have their notebooks set up, so it is done as a worksheet.
Then we move on to geometry!
Points, Lines, and Planes Introductory Vocabulary
Our very first set of notes is a foldable about the most basic and important geometry vocabulary. We use a foldable to complete definitions, analyze diagrams, and note the notation for point, line, plane, line segment, ray, and angle. Foldables are a fantastic study aid that allows students to quiz themselves. Completing this foldable does not take a full class period. We pair filling out this foldable with a card sort, matching a definition, diagram, and the notation with each vocabulary word.
Collinear vs. Coplanar & Intersection Postulates
For our next page, we define collinear and coplanar. These are not important vocabulary words, but they do allow students to further analyze and discuss diagrams. Also, in the lesson, we see how lines and planes intersect one another. This is not critical information for our course. Of the three postulates we study, the only one we really need to know is that two lines intersect at a point. This part of the lesson also allows students an opportunity to analyze diagrams.
Line Segment Measures
Then, we move on to apply equation solving to Geometry topics. We begin with the segment addition postulate, and practice drawing diagrams from descriptions, writing equations, solving equations, and using substitution to complete a problem. Next, we define bisect and segment bisector before applying the concept to equation solving. Lastly, we define midpoint, and apply midpoints to writing and solving equations.
Angle Measures
For our next class, we work with the angle addition postulate after discussing the protractor postulate. For this lesson, I have the angles drawn for students so they can focus on identifying the angles correctly. At first, students often struggle with knowing where to write the expression that represents an angle. Next, we define angle bisector and practice applying angle bisectors. Then, we move on to practice problems that integrate both the angle addition postulate and angle bisectors.
Geometry Interactive Notebook: Angle Pair Relationships
Our next lesson, angle pair relationships, is the most important part of the lines and angles unit. We will see these angle pair relationships repeatedly throughout Geometry. In this lesson, we define adjacent angles, complementary angles, perpendicular lines, supplementary angles, linear pair, and vertical angles. We practice applying each of these definitions, using diagrams, word problems, and ratios. We spend the most time on the linear pair postulate and the vertical angles theorem, even mixing the two together. The linear pair postulate and vertical angles theorem will be necessary to complete proofs and to solve advanced algebraic problems in Geometry. After we complete these notes, we spend at least one more day just practicing identifying and applying these angle pair relationships.
Geometry Interactive Notebook: Parallel Lines
The other major topic in our unit, parallel lines comes next. We start by defining parallel lines and transversal, then we explore the angle relationships formed by parallel lines and a transversal. We focus on corresponding angles, alternate interior angles, alternate exterior angles, and same-side interior angles. After describing where to look for the relationship (ie: I say to students “alternating means on both sides of the transversal”, and “what does interior mean?”), students identify a pair of angles that meet the criteria of the relationship. In our geometry interactive notebook, we use different colored highlighters for each pair of angles that match the criteria. Then students determine if the angles are congruent or supplementary just by comparing the size of the angles they identified.
For our first practice problem, students are given the measure of one angle, and they have to find the rest of the angles formed by a set of parallel lines cut by a transversal. They also have to explain their reasoning. Here, students get to review the previous lesson on angle pair relationships, while incorporating the new topic. Then, students have a few examples identifying the angle relationship, and then writing and solving an equation. Next, students are challenged by some problems involving parallel lines and transversals that do not look like the first few we did. This set of challenge problems is great for starting conversations. After completing this page, we practice parallel lines for two more days.
Algebraic Line & Angle Proofs
For our next geometry interactive notebook page, we apply the postulates and theorems we learned about lines and angles to algebraic proofs. We start with a graphic organizer that shows the different concepts we learned throughout our lines and angles unit that can be given to us when we start a proof. In the graphic organizer, we are also given the conclusion that we can come to based on each given. (These would be a statement in a proof.) We work together to identify the property/definition/postulate/theorem that the given and conclusion are referring to. (These would be the reason in a proof.)
Remember, prior to this lesson, students already practiced algebraic proofs. Now, we are adding in a property/definition/postulate/theorem about lines and angles to start the proof. What I noticed, is that once we figured out the property/definition/postulate/theorem being used and set up an equation, students did not need any more help. They were able complete the rest of the proof not their own.
Line and Angle Proofs
Finally, we moved on to our last topic of the unit, line and angle proofs. For this lesson, we start with a few rules for two column proofs. Then, we list the reasons that line segments may be congruent, and that angles may be congruent or supplementary. We also discuss differences that students will encounter in notation. I do not emphasize this when students are writing their own proofs. If a student forgets to put an m in front of the angle symbol when they mean the measure of an angle, I would never take away points. However, I want to make sure students understand why the letter m may or may not be present when they see a proof.
Then, we complete 4 proofs. This is the first time students encounter proofs without numbers. (Although, I do use two examples with 180 degrees for the sake of ease and familiarity.) So, I make sure to include blanks that students can fill in, some steps to guide them, and the number of steps required to complete the proof. Fill-in-the-blank proofs require following some else’s train of thought, and this is a skill that I need to teach.
Geometry Interactive Notebook: Lines and Angles Resources
Are you looking for materials to teach this unit? Look no further! All of the pages you see in my Geometry Interactive Notebook: Lines and Angles are now available. Prior to uploading these pages for your use, I taught each lesson as described above. Some of the pages may not look exactly as they do in this post because they have all been edited and updated. Also, a full answer key for each page is included.
Looking for more resources? Check out my interactive notebook resources page!
