- Students are to find a picture that illustrates an example of parallel lines and perpendicular transversals.
- Then, students need to cut out the picture.
- Label all of the angles.
- Label all of the measures of all of the angles.
- Finally, ask students to explain how the converse theorems impact the perpendicular lines in each picture.
- If time allows, you can request that students work with more than one picture.
- You can also extend this activity to include a presentation piece, so that students are required to verbalize what
they have learned through the activity.
III.MeetingObjectives
- Students will identify perpendicular transversals and parallel lines.
- Students will identify the angles associated with perpendicular transversals and parallel lines.
- Students will identify the converse theorems associated with parallel lines and perpendicular transversals.
IV.NotesonAssessment
- Have the students selected an appropriate picture?
- Does this picture show parallel lines and perpendicular transversals?
- Are all of the angles accurately labeled?
- Have the students made notes of the converse theorems involved?
- Assess student understanding through written work and presentations.
Non- Euclidean Geometry
I.SectionObjectives
- Understand non- Euclidean geometry concepts.
- Find taxicab distances.
- Identify and understand taxicab circles.
- Identify and understand taxicab midpoints.
II.ProblemSolvingActivity-TaxicabGeometry
- In this activity, students are going to work on the following problem. This can be done individually or in pairs.
- Here is the problem.
- “Juan rides his bike 2800 feet from him home to the park to play baseball. Using a scale of 1 unit: 200 feet,
draw a possible path for Juan on a coordinate grid.” - Students will need to work backwards to solve this problem.
- There are several different solutions to this problem.
- The important thing to note is that Juan travels 14 units according to the scale.
- Any combination of Juan traveling a combination of 14 units is correct.
- You will get many different pictures of this problem.
- Allow time for the students to share their work and explain how they got their answers.
- Extension of this is to say that Juan travels 5,820 feet to school. This is the equivalent of one mile. Give the
students the same scale and see what they can do with it. - Have students draw a diagram.
- The solution is that Juan walks 29.1 units to school. There are many different diagrams that could come out
of this problem. Watch for the.1 in the diagram too.
5.3. Parallel and Perpendicular Lines