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Throughout lesson 2.1-2.8 we learned a lot.   I think that all of our lessons revolved around proofs. Each lesson taught us a new way to figure out steps in a proof. I know that although I can get confused with the wording for some theorems/reasoning , they are good to know.  With more practice, I will be able to utilize them when it is appropriate to do so in a proof!

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LT 6
I can apply the  addition  properties of segments and angles.

As seen below segment PQ is 10 and so is  segment ST.   Therefore they are congruent.  Segments QR and TU are both 4.  Therefore they are also congruent. So if PQ was added to QR the total would be 14.  If ST was added to TU the total would be 14.  So both segments PR and SU are equal to 14, meaning that they are congruent.  We can sum this all up by saying:  If congruent angles/segments are added to congruent segments/angles, then their sums are congruent.

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LT 7
I can apply the subtraction properties of segments and angles.

Below it states the theorem that matches this learning target. Basically knowing that segments and angles are congruent, can help you to find a lot of information. Since two angles/segments are congruent, other segments/angles that are also congruent (or the same ) subtracted from them will definitely lead to two differences which are congruent. In the example below, segments QS and RT are both equal to 10.  They both overlap by 3.  So,  if you subtracted the three from the 10, you know that the differences are 7 ( both the differences are congruent).  Therefore segments QR and ST are equal to 7.

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LT 11
I can recognize opposite rays.

Opposite rays are rays that have to follow two rules. One: they need to lead in opposite directions (facing away from each other). Two: they need to have the same endpoint.  In this example it is listed that ray AB and ray BC are opposite rays, but if that was not included, then we can use these two rules to figure out if they are opposite. They both go in opposite ways from each other, and they have the same endpoint (B). Therefore these two rays are opposites.

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LT 12
I can recognize vertical angles.

Vertical angles are angles they are opposite of each other/ reflected over a intersection of two lines. The more I use this idea in proofs, the more clear it will be to me when vertical angles are present. In this image, the corresponding colors are vertical angles. The purple angles are vertical to each other and the blue angles are vertical to each other. Another important trait of vertical angles is that they are congruent.

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LT 9
I can apply the transitive properties of angles  and segments.

Below includes the theorem matching the transitive property. Corresponding to that we see a example of the transitive property in use. As seen in the givens,
angle 1 is congruent to angle 2. We also know that angle 2 is congruent to anlge 3. One way to look at that is by plugging in numbers into the problems to help make more sense of it. By plugging in 30 degrees into angle 1 we know that angle 2 is equal to 30 degrees. If angle 2 is 30 degrees, then we know that angle 3 is also 30 degrees. So then we can conclude that angle 1 is congruent to angle 3.  So relating this back to the learning target, we can understand that 2 angles are congruent if they are congruent to the same angle.
This can also be applied to segments.

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LT 5
I can prove angle congruent by using complementary and supplementary angle theorems.

Below there are two photos that show a nice example of this learning target. As you can see in the first picture, angle B and C are congruent. Although, angle D and angle A are both complementary to these congruent angles. So, if two angles are complementary to congruent angles, then they are congruent. In the second picture, angle C and A are both complementary to the same angle. So, if two angles are complementary to congruent angles, then they are congruent. (Reflective property used to show that angle B is congruent to angle B.) As you can see both of these pictures show great problems. These problems can also be translated into supplementary problems. If they were, than the conclusion would be very similar; If two angles are supplementary to congruent angles, then they are congruent. I like these two photos and they can do great review.

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LT 5 Continued

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LT 14
I can copy an angle.

This here is an awesome video.  The video is a cool simulation of how to construct an angle.  What I like about this video is that it gives every single step played out that one should take when copying an angle. The steps they show are:
1.  Measure the given angle's opening arch.
2. Draw a new line.
3. Copy down the angle's opening arch on that new line.
4.  Measure the exact point to point measurement on the opening of the given angles arch.
5. Copy down that exact measurement of the angles arch on the new angle.
6. Now that the copied angle has the exact measurement of the  opening arch, you can draw a straight line to make the missing ray of the angle.
Once again, this video is quick and easy, but it can help to implant the order of steps needed to copy and angle into your brain.

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Learn how to construct a Congruent Angle using just a compass and a straightedge

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LT 3
I can recognize complementary and supplementary angles.

This image below shows a chart. This chart gives an example of both supplementary angles and complementary angles. This table also shows how in complementary angles, two (adjacent) angles add up to 90 degrees (52 degrees + 38 degrees). They then are the complements of each other. Although supplementary angles are two (adjacent) angles that add up to 180 degrees (128 degrees + 52 degrees) . They then are the supplements of each other.  This table is cool because it can continue to remind me the definitions of supplementary and complementary angles. Knowing those definitions are important because you need to be able to apply those ideas to certain problems weather they are solving problems or proving problems.

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LT  2
I understand the concept of perpendicularity.

This picture shows the concept of perpendicularity.  As seen in the picture, line  DC is perpendicular to line AB.  This picture also matches the idea of:  If two lines intersect to make right angles, then they are perpendicular.  (As you can see when lines AB and DC intersect, they make 90 degree angles, so that means that they are right angles.)  I think that the concept of perpendicularity is very helpful to understand  when making a proof or finding measurements of angles.  What I mean is that when a problem gives you clues , for example:  two lines/segments being perpendicular,
then you should understand that the angles that are a result of the intersection are right angles/90 degrees. So in conclusion, this picture shows a simple example of two lines that are perpendicular which will hopefully remind me of the key ideas behind perpendicular lines.

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LT 13
I can copy a segment.

Below are step by step instructions on how to copy a segment. These are cool instructions because they give a description and picture for each step.  These can help me to remember the few steps it takes to make a segment.  This link explains steps that include:
1. Measuring the given line segment with a compass.
2.  Drawing a new striaght line.
3.  Taking the original measurement of the segment, and drawing a new arch on the line you had just created.
4. Creating new points to show the new line segment.
This is just a simple chart with steps but it can help so much when reviewing this learning target.

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Printable instructions for copying a line segment with compass and straightedge or ruler

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Printable step-by-step instructions for copying a line segment with compass and straightedge or ruler