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This course has encouraged me to break away from the monotony of lecturing and worksheets all day every day. With the inclusion of alternative assessments through prezi and voice thread it really makes the class more dynamic. This and the inclusion of non-academic and academic videos brings in another voice besides me into the classroom to let the students learn in different ways. Integrating technology in a technology rich world is a no brainer and helping the next generation to be more knowledgeable in it not only helps out the students, but helps the other generations in having people that can add new things to the web and enrich all of our lives.

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1a, 1c, Creativity and reflection in the prezi. 2b,c,d students are working and are assessed in different ways 3a,c,d using different technological systems and model tools. 4a,c working to create a more ethical and safe virtual environment with voice thread and other tools. 5b,c working to create a tech infused environments.

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2a, students creating a voice online and being a citizen. 6a,b,c,d Students communicate through technology and communicate on appropriate platforms and engage. 7a, students are working with online resources and voice threads to work with others.

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1b, 1c, creating their own environment via khan and prezi. 3a, 3b, Researching information for the Prezi. 4b, 4c, working with prezi and their designs.

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Explain in your own words how to find a parallel and perpendicular line. Also if you have any questions submit them via voice thread!

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design discussions
no-schedule meetings
professional development
collaborate with clients
sales and marketing

replace text-only discussions
interactive lectures
support UDL principles
no-schedule office hours
professional development

student presentations
conversational practice
professional development
rich assessment
safe and accountable

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Transforming media into collaborative spaces with video, voice, and text commenting.

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Here is a video for the Intro to slope!

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Sal shows how to find the slope of a line.

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                                                                                                                               Questions?

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                                                                                                                               Questions?

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Add a question below!

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Mr. Ruiz, I don't like the parallel one!

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Mr. Ruiz, I don't like the parallel one!

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That is fine, let's try a different way. Still start by creating that angle, we will need that! Next act like you are creating a bisected angle. Make an arc that reaches from your point to the line. Anchor where they meet, and then make your X. Instead of connecting through the vertex like an angle bisection, connect the line from the X to the point off the line.

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Yes! this one is rather tricky. First you need to create an angle. Then create an arc smaller than your point. Create the same arc approximately the same same height and same length away. You then have to measure the arc, and anchor where the arc meets the point past the line. You have to create an X there, and then you can connect through the point and X.

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Learn how to construct a Parallel Line through a Point using just a compass and a straightedge

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Here we have a point NOT on the line. Essentially what we want to do is create an arc that will bisect the line at two points. After that we use those two points as anchors to make the X's and connect through the line.

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Perpendicular to a Point NOT on a Line Construction

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Learn how to construct a Perpendicular to a Point NOT on a Line using just a compass and a straightedge

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Lets start simple with a point on a line. First we create the endpoints with our compass. After that it is essentially re-bisecting the line from those points. Here is the video for it.

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Learn how to construct a Perpendicular to a Point on a Line using just a compass and a straightedge

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How to construct a Line Segment Bisector AND a Right Angle
using just a compass and a straightedge

images/construct.js?mode=linebisect

Steps:

Place the compass at one end of line segment.

Adjust the compass to slightly longer than half the line segment length

Draw arcs above and below the line.

Keeping the same compass width, draw arcs from other end of line.

Place ruler where the arcs cross, and draw the line segment.

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Learn how to construct a Line Segment Bisector AND a Right Angle using just a compass and a straightedge

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Learn how to construct an Angle Bisector (halve the angle) using just a compass and a straightedge

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Yes! In unit 1 we bisected angles and lines to make congruent angles and midpoints. If you need a refresher look up these videos.

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What are constructions? They are using compasses to do fun things like bisecting lines and angles! Since we have already done them in the past, we are moving on to creating perpendicular lines from a point on, and off a line to the line parallel to it. We will also be constructing Parallel lines!!!

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Yes! This is why we teach it! 3.6 and 3.7 are G-GPE.B.5, which means that our goal is to prove perpendicular and parallel lines and apply them to geometry.

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We have standards that we need to reach. Currently these are the ones that are for 3.1-3.3:
G-CO.A.1 and G-CO.C.9
These are saying that students should be able to know precise definitions of the academic vocabulary they are using, and solve theorems about congruence involving lines and angles.

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Look at the questions below and decide if they are perpendicular, parallel, or neither.

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For this use, you need to plug in the coordinates the same way, but this time you are only finding the b. After you find the b, you use that and the slope you have to re-make a new equation.

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In Point slope form you can use the equation:
Y-Y1=M(X-X1)

For this you plug in the (X,Y) coordinates you have into the X1 and Y1 spots. The M is your slope.

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In previous years classes you went into detail about how to find the slope. It started with Rise over Run, and the change in Y over the change in X. You can find the slope and the Y intercept with different formulas. There are two different ways. Point slope and Y=MX+b

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Parallel Slopes and Perpendicular Slopes

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Parallel Slopes and Perpendicular Slopes

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Earlier we talked about Parallel and Perpendicular lines. Now let's go more in depth and talk about their slopes.

-Parallel lines have the same Slope, but have different Y intercepts. An Example would be two lines. One 3X-4 and the other 3X+2.

-Perpendicular Lines have opposite reciprocal slopes. This means that the slopes are flipped over, and their signs change. This would be like a line with the equation 2X-1 and a line -1/2X +2

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Lets let Jay Z take us on to the next section!

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Now it is time for you to create! Make a Prezi about the angle relationships to share with class. Make sure you use Corresponding, Alternate Exterior, Alternate Interior, and Same Side Interior.  Look online for other examples that work for you.

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Open Canvas

Create, organize, and move freely on an open canvas. Create seamless presentations without the restrictions of linear slides.

Ready-made asset libraries

Choose from millions of images, stickers, GIFs, and icons from Unsplash and Giphy.

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Presentations and videos with engaging visuals for hybrid teams | Prezi Present

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Welcome to Prezi, the presentation software that uses motion, zoom, and spatial relationships to bring your ideas to life and make you a great presenter.

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Here is a little video to Explain perpendicular, and parallel lines.

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Let's think a little bit about two terms that you'll see throughout your geometry, and really, mathematical career. One is the idea of things being perpendicular. And usually, people are talking about perpendicular. Actually I'm misspelling it-- perpendicular lines, and the idea of parallel lines. So perpendicular lines are two lines that intersect at a right angle. So what am I talking about? So let's say that this is one line right over here and that this is another line right over here. We would say these two lines are perpendicular if they intersect at a right angle. So they clearly intersect. In order for them to intersect at a right angle, the angle formed between these two lines needs to be 90 degrees. And if any one of these angles is 90 degrees, the rest of them are going to be 90 degrees. So this is 90 degrees, then these are perpendicular lines. And if that's 90 degrees, then that's going to be 90 degrees, that's going to be 90 degrees, and that's going to be 90 degrees. So if any of them are 90 degrees, the rest of them are 90 degrees, and we have perpendicular lines. If you have two lines that on a two-dimensional surface like your paper or like the screen never intersect, they stay the same distance apart, then we are talking about parallel lines. So this line right over here and this line right over here, the way I've drawn them, are parallel lines. They aren't intersecting. They're both kind of going in the same direction, but they're kind of shifted versions of each other. They will never intersect with each other. So these two are parallel. If we have two lines that, let's say, they intersect, but they don't intersect at a right angle, so let's say we have that line and we have this line right over here, and they're clearly not intersecting at a right angle, then we call these neither perpendicular nor parallel lines. These lines just intersect.

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Parallel & perpendicular lines intro | Analytic geometry (video) | Khan Academy

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Let's think a little bit about two terms that you'll see throughout your geometry, and really, mathematical career. One is the idea of things being perpendicular. And usually, people are talking about perpendicular. Actually I'm misspelling it-- perpendicular lines, and the idea of parallel lines.

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We talked about lines being parallel, but what if they are not? We also need to teach about Perpendicular and Skew.
-Perpendicular are when angles cross to make a 90 degree angle.
-Skew is when two lines are not coplanar and do not cross.

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These are terms that we should know from the previous unit to help us now.
Supplementary- Add up to equal 180 Degrees
Linear Pair- A pair of angles on the same line that are supplementary.
Vertical Angles- Angles that are across from each other and are congruent.
Coplanar- When lines or points are on the same plane.

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All of these that have the special names all have special properties. The angles that are corresponding, Alternate Exterior, and Alternate interior all are congruent angles. This means that the angles are of the same measure. The Same side interior are the different ones. These are the angles that add up to equal 180.

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We are staying between the lines again (Interior) and this time are staying on the same side of the transversal (Same Side). Examples are 9 and 10, and 8 and 11

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Same Idea as alternate interior, but on the outside of the parallel lines. Examples are 7 and 13, and 6 and 12.

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Alternate Interior angles are angles that are inside the two parallel lines (interior) and on alternate sides of the transversal (Opposite sides). Examples are like angles 8 and 10, and 9 and 11.

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Angles are corresponding when they are stacked above each other, and on the same line as the transversal. Examples are numbers like the pair 6 and 10, and the pair 8 and 12.

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When a transversal cuts a pair of parallel lines they create special pairs.

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What Makes a line Parallel? Parallel lines are lines that never touch and have the same slope

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Talk to OT Genesis if you need some help!

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twitter @kingchris232 cut it remix made by me

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We are working in this unit with angles and Transversals! What is a Transversal? It is a line that Cuts another line or two.