Angles and Parallel Lines (Day 2 of 2)
Lesson 12 of 16
Objective: SWBAT understand angle measure relationships associated with two lines cut by a transversal.
Sometimes it's worth spending a good amount of class time going over the homework assignment given the previous day. Today is one of those days in my class. So, during today's Launch, I will first walk around checking students' homework for completion (HW Angles and Parallel Lines) and answering quick question. Then, I will display the homework using the document camera. This allows me to call on students to write answers on the whiteboard (as long as I take care to keep the camera and image still).
I begin with the true or false questions. I make sure each student explains their reasoning, and, provide an example that proves that the statements in Questions 1 and 3 are false. For questions 4 and 5, I make sure that the students correctly identify the transversal and the two lines it intersects to form the angle pairs.
Finally, I call on some student volunteers to fill the table. At this point, I expect that some students may write that alternate interior angles are in a Z and corresponding angles are in an F, either right side up, or flipped. I accept these answers as long as they are able to draw, label and identify the lines and transversal that form them.
After we complete the homework review, I will ask each student to pair up with the same partner they had the previous day. As they sort themselves, I will hand each student a copy today's Application Activity. In this activity, students will measure the angles in each figure using their protractors. Once all the angles in a figure are measured, they will describe the angle relationships that exist. I give the class about 20 minutes to work and write their answers.
I walk around the room listening to make sure that the appropriate vocabulary is being used (MP6). My students are still learning the names of angle pairs, so I will give them clues like, “same position” (for corresponding angles) or “different sides of the transversal” (for alternate interior angles). I always like to ask students if it matters how long the lines are? Another question I like to extend is, "Can lines a and b (see Questions 1 to 3) be rotated in different directions?"
I am hopeful that my students will come up with the following conclusion:
In order for the two lines to be parallel, the corresponding angles must be congruent, alternate interior, and exterior angles must be congruent, and same side interior angles must be supplementary.
To close today's lesson I choose groups and pair them up so as to have four students per group. The goal of this closure activity is for students to exchange papers and discuss the work by other students as the worked on the activity.
As they review their peers' work, I encourage students to look for ideas in the other group's work that they may have overlooked. I ask them to make suggestions and/or corrections if necessary. I give groups a few minutes for this discussion and interchange of ideas. As they work, I walk around listening, making sure that students are making correct conjectures and conclusions. I am also ready to mediate disputes about an answer (if necessary).
At the end of the discussion, to finalize the lesson, I will go up to the board and write:
IF TWO LINES ARE PARALLEL, THEN...
Then, I will ask each group to write all the conclusions that can be drawn from this statement based upon our work over the last couple of days. Students will write the list of conclusions on the back of their activity sheet (or on a clean sheet of paper).
I hope that students will record the following conclusions:
- Same side interior angles are supplementary
- Alternate interior angles are congruent
- Corresponding angles are congruent
- Alternate exterior angles are congruent
It is important to tell students that by simply observing a diagram, one cannot conclude that the lines being intersected by a transversal are parallel or not. Unless the information is given, measured, or proven by mathematical means, we should not make assumptions. We must be prepared to measure angles when told to do so, or if we want to make a conclusion about the relationship between two angles.
In tonight's Homework Assignment, however, the measurements are given. So, I remind students to use the given information, not to measure the angles in the first diagram. In other words, assume the measurements are correct and use the given measurements to answer the questions.
Teacher's Note: Some students may not remember that the "m" before the angle symbol (m<) means 'the measure of", so I always try to remind students of this notation.
The following extension can be given to students as a challenge for extra credit.
Two lines are cut by a transversal. Of the eight angles formed, four of them measure 25 degrees and four measure 155 degrees. However, none of the lines are parallel. Draw a sketch that illustrates how this is possible.
Sample Sketch: Extension for Extra Credit.docx