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I chose this source because it shows how to organize information from word problems.

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How Do You Solve a Problem by Making an Organized List? | Virtual Nerd

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Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear system, users are free to take whatever path through the material best serves their needs. These unique features make Virtual Nerd a viable alternative to private tutoring.

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I chose this source because it shows how parallel and perpindicular slopes relate

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Learning Objective(s)
· Define perpendicular lines.

· Recognize and create graphs and equations of perpendicular lines.

are two or more lines that intersect at a 90-degree angle, like the two lines drawn on this graph, and the x and y axes that orient them.

Perpendicular lines are everywhere, not just on graph paper but also in the world around us, from the crossing pattern of roads at an intersection to the colored lines of a plaid shirt. In our daily lives, we may be happy to call two lines perpendicular if they merely seem to be at right angles to one another. In algebra, we use equations to make sure of it.
Recognizing Perpendicular Lines
Let's compare the equations of lines that are perpendicular and those that are not to see if there is a pattern that will allow us to recognize perpendicular lines. We'll start with two lines that we know are not perpendicular.

Line A has an equation of , and Line B has an equation of . These two lines are clearly not at 90-degrees to one another. Do you see any connection between their equations?

If you couldn't find anything-you're right. There isn't any link between the or [y-intercepts] of these lines.

Now let's look at two lines that are perpendicular:

On this graph, Line A has the equation of and Line B has the equation of . Do you see any connection between these equations?

If you said no again this time, you missed something. It's a little tricky, but there is a relationship between the slopes of these two lines. The slope of Line A is , and the slope of Line B is . These numbers are opposite reciprocals. An opposite reciprocal is the fraction form of a number flipped upside down (that's the reciprocal part), and with its sign changed (that's the opposite part). Write those slopes side by side and it becomes more obvious: and are opposite reciprocals.

This is the defining feature of the equations of perpendicular lines-the slopes of perpendicular lines are opposite reciprocals.
Creating Perpendicular Lines
Now that we've learned what perpendicular lines have in common, let's see if we can use that knowledge to create the perpendicular to a given line. Spend a few moments moving the red line on the graph below, and see if you can make it perpendicular to the blue line. The slider bar marked m will let you manipulate the slope. First, figure out the slope of the blue line, then change the value of m to the opposite reciprocal of that number. Do the lines look perpendicular to you now?

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser ( Click here to install Java now)

Now try changing the value of b, which is the y-intercept of the red line. Do you see that there are an infinite number of perpendicular lines? It doesn't matter what the y-intercepts are, lines are perpendicular as long their slopes are opposite reciprocals of one another.

To create a perpendicular line from an equation, we once again start by identifying the slope of the original line. Then we write a second equation, changing the slope to the opposite reciprocal of the slope in the original equation.

A) and

B) and

D) all of the lines are perpendicular

Perpendicular lines are lines that cross one another at a 90° angle. They have slopes that are opposite reciprocals of one another. Unlike parallel lines that never touch, perpendicular lines must intersect.

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Learning Objective(s) · Define perpendicular lines. · Recognize and create graphs and equations of perpendicular lines. are two or more lines that intersect at a 90-degree angle, like the two lines drawn on this graph, and the x and y axes that orient them.

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I chose this source because it is the section from our book that shows how to relate slope to orientation on the coordinate plane

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I chose this source because I think that it very clearly explains the concept of slope and also shows how to calculate it.

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The Slope of a Straight Line | Purplemath

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Explains the slope concept, demonstrates how to use the slope formula, points out the connection between slopes of straight lines and the graphs of those lines.

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I chose this source because it shows all of the different kinds of angles formed by transversals

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This packet will teach you about transversal lines, alternate interior angles, corresponding angles, same-side interior / consecutive angles, and alternate exterior angles. This packet includes diagrams and notesheets to show the relationships between the angles created by two lines and a transveral line.

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I chose this source because it has good pictures of transversals

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I chose this source because it has a lot of information on planes

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except that the paper itself is not a plane, because it has thickness! And it should extend forever, too.

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I chose this source because I found it gave a simple way of explaining how to find a perpendicular bisector using equidistance

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Using Two Equidistant Points to Determine a Perpendicular Bisector

By Mark Ryan

You can use two equidistant points to determine the perpendicular bisector of a segment. (To "determine" something means to fix or lock in its position, basically to show you where something is.) Here's the theorem.

Two equidistant points determine the perpendicular bisector: If two points are each (one at a time) equidistant from the endpoints of a segment, then those points determine the perpendicular bisector of the segment. (Here's an easy way to think about it: If you have two pairs of congruent segments, then there's a perpendicular bisector.)

This theorem is a royal mouthful, so the best way to understand it is visually. Consider the kite-shaped diagram in the above figure.

The theorem works like this: If you have one point (like X) that's equally distant from the endpoints of a segment ( W and Y) and another point (like Z) that's also equally distant from the endpoints, then the two points ( X and Z) determine the perpendicular bisector (line XZ) of that segment (segment WY).

Here's a " SHORT " proof that shows how to use this equidistance theorem as a shortcut so you can skip showing that triangles are congruent.

You can do this proof using congruent triangles, but it'd take you about nine steps and you'd have to use two different pairs of congruent triangles.

Reason for statement 1: Given.

Reason for statement 2: If angles, then sides.

Reason for statement 3: Given.

Reason for statement 4: If two points ( S and O) are each equidistant from the endpoints of a segment (segment RH), then they determine the perpendicular bisector of that segment.

Reason for statement 5: Definition of bisect.

Reason for statement 6: Definition of midpoint.

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Using Two Equidistant Points to Determine a Perpendicular Bisector - dummies

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You can use two equidistant points to determine the perpendicular bisector of a segment. (To "determine" something means to fix or lock in its position, basically to show you where something is.) Here's the theorem. Two equidistant points determine the perpendicular bisector: If two points are each (one at a time) equidistant from the endpoints ...

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I chose this source because it wrote out how this learning target works instead of just showing an example

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SOLUTION: prove that any two right angles are congruent

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put this solution on YOUR website! There is a THEOREM,,,," If two angles are supplements of congruent angles(or the same angle), THEN the two angles are congruent. . In this case,,,the "same angle" is 90 degrees. . Both of the right angles are supplements, . Therefore the right angles are congruent, .

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I chose this because I thought that it really elaborated on how to use the midpoint formula

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Demonstrates how to use the Midpoint Formula, and shows typical homework problems using the Midpoint Formula.

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I chose this source because I think it demonstrates how to do a detour proof very clearly

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4.1 Detour Proofs and Midpoints (Lesson)

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A lesson on detour proofs (proofs of congruent triangles that are contingent on proving prior pair of triangles congruent) and on the formula for finding midpoints in a coordinate plane. The video also covers the use of the midpoint formula in a worked example requiring the development of an equation of the median of a triangle.