3.6 Parallel Lines in the Coordinate Plane What have you learned so far about parallel lines in chapter 3?

What are Parallel Lines “Lines that never touch in the same plane” “2 lines that lie in the same plane that will never intersect” “Two lines that are coplanar but never meet” “Two lines that never intersect and are not touching” “Never touch, point exactly the same direction” Always equivalent, meaning they always have the same measure and will never intersect” These are the definitions of Parallel Lines that the students gave me the day before when I did a pretest of their knowledge. We will look at these before and after we address this part of the lesson. When we look at them now I just ask the students to think about them and reflect on them.

What is slope? How do you find it? This is a class discussion. I’m looking to see what the students know.

Rise over Run? (5,3) and (7, 8) What if you just have two points? This introduces the equation for finding slope. Slope equals (y two minus y one) all over (x two minus x one).

Find the slope of line A and line B. Discuss and check your results with a neighbor. What did you discover? I asked each student to find the slope of the two lines and then check their answer with a neighbor. We will come back as a group, share our answers and work the problem out.

Lets try this one more time… Same as previous slide.

This is bringing in what they’ve learned from the earlier lessons about what makes two lines parallel. There is a app that the Promethean board has that I can place a protractor on top of these two angles and see if they have the same measure. This is verify that they are parallel on top of them having the same slope. CORRESPONDING ANGLES!!

y=mx+b What’s the formula for a line? What does m stand for? (In slope intercept form) y=mx+b What does m stand for? What does b stand for? Now we will find the equation for these two lines and see the relationship between their slopes in the equations.

y=mx+b This is extra room to work out the equation of the second line.

What are Parallel Lines “Lines that never touch in the same plane” “2 lines that lie in the same plane that will never intersect” “Two lines that are coplanar but never meet” “Two lines that never intersect and are not touching” “Never touch, point exactly the same direction” Always equivalent, meaning they always have the same measure and will never intersect” Here we look back at what the students said earlier that parallel lines are and address the definitions. There are certain parts of the last three that I will address. On the fourth definition I will emphasize that the lines cannot be the same line. On the fifth I will point out that “the same direction” hopefully means slope, and if so it is correct. On the sixth definition, the lines are not always equivalent, the two lines cannot be the same line and be parallel, they can’t touch.

Postulate 17 Slopes of Parallel Lines (Pg. 166) In a coordinate plan, two nonvertical lines are parallel if and only if they have the same slop. Any two vertical lines are parallel. Coplanar Same slope If the students haven’t written anything down, I want them to write this down. This is the Postulate that we have just gone through with our earlier activities.

3.7 Perpendicular Lines in the Coordinate Plane What have you learned so far about perpendicular lines in chapter 3?

What are Perpendicular Lines? “2 lines that intersect to make 4 90 degree angles “2 straight lines that are on the same plane and intersect at a 90 degree angle” “Perpendicular lines meet a point where all angles are 90 degrees” “Two lines that intersect at one point.” “Two lines that cross at come point and all 4 angles created are 90 degrees. Line bisects a straight angle.” Like earlier, this is what the students said earlier about perpendicular lines.

This is an activity for the students to see that perpendicular lines slopes are negative reciprocals of each other. They will be given an piece of paper with a coordinate plane and they will be given and 3x5 card. I will do this activity on my own sheet of paper under the projector thing my teacher has that shows what I’m doing at the desk on the promethean board. They will put the 3x5 card in an intersection where the lines on the coordinate plane hit and will trace the lines from the 3x5 card.

Then they will find the slopes of each line. Then we will rotate the 3x5 card and use two different lines. I will ask for the student’s data on what the slopes of each of their lines are and put them into a table that I draw on the board. This way they can see the corresponding slopes for each line. Then we will discuss what we notice about the slopes. When I taught this lesson it was really cool to hear their discussion and hear them discovering the connection.

y=mx+b Here we will develop the equation of the two lines that I have up here. I will have them work it out at first on their own, and then we will work through it together on the board.

What are Perpendicular Lines? “2 lines that intersect to make 4 90 degree angles “2 straight lines that are on the same plane and intersect at a 90 degree angle” “Perpendicular lines meet a point where all angles are 90 degrees” “Two lines that intersect at one point.” “Two lines that cross at come point and all 4 angles created are 90 degrees. Line bisects a straight angle.” Now we go back and look at what they said when they were asked to define perpendicular lines in their own words. I would really highlight the end part of the fifth definition. I was really impressed by this answer and thought it was interesting.

Postulate 17 Slopes of Perpendicular Lines (Pg. 166) In a coordinate plane, two nonvertical lines are perpendicular if and only if the produce of their slopes is -1. Coplanar Slopes are negative reciprocals Here, like before, if there is something at all that these students write down it will be this. This is the postulate that we just explored.

Now how well do you know the information? What are two things that have to be true for two lines to be Parallel? What are two things that have to be true for two lines to be perpendicular? What is the slope of a line containing the points (-2,6) and (0,1)? What’s the equation of a line with a slope of 1/3 and a y-intercept of -4? Write an equation of two lines that are parallel. Write the equation of two lines that are perpendicular. The answers to this will be put on their 3x5 card and I will also ask them to write any questions they had about this lesson that they didn’t understand.