1-5.) Think about a number line. Adding numbers means going further up the number line, subtracting means going further down the number line. Adding a negative means going further down the number line. Think of subtracting a negative as the opposite of going down the number line, which would be going up the number line.
6 and 7.) Subtract something from both sides 8.) multiply on both sides
9.) add something to both sides (add to get rid of a negative number)
10.) Combine like terms on the right side (negative and a negative stays negative), then subtract or add to both sides, and you should get “something x” equals zero. What is zero divided by any number? ZERO!
11.) Get your x’s on the same side of the equation (subtract from both sides), then get x by itself.
12.) (skipped by accident) 13.)Distribute and simplify, then get your x’s together, and get x by itself
14.) Just draw two separate line segments. One of them has endpoints A and B, the other has endpoints C and D. The congruence sign tells you that AB and CD are congruent (have the same length). We show congruence on a diagram by using tick marks!
15.) Draw a point E and a point G, connect them with a line segment, put point F right in the middle. Since it is exactly in the middle, EF and GF are the same (congruent), so mark that on your diagram with tick marks!
16.) Between doesn’t mean exactly in the middle! Draw points A and B and make Q anywhere on the line segment connecting them.
17.) Draw an angle ABC and an angle DEF, but make them the same size and put an arc mark on both of them, because that’s how you show congruent angles.
18.) Draw angle MNO first. Now put a dot anywhere inside the angle (not on one of the rays, but anywhere in-between the rays). Name this dot R.
19.)Draw angle XPZ. Now recall that bisect means to split in half. From the vertex P, extend a new ray that splits the size of the angle in two equal halves. Just make sure that you label another point Y on this new ray.
20.) Draw a line, with the arrows going in both directions. Now create a ray coming off of the line in any direction. Do you see the two angles created? Those angles form a linear pair. Label them 1 and 2.
21.) Draw two angles and make them not connected.
22.) Draw a line. Put points A, B, and C all on it!
23.) Create three points, just make sure you can’t draw one line that connects all three!
24.) For rays, the order we write the points in matters! Ray OG means that O is the endpoint and the ray extends through point G.
25.) The idea is that we have distance between points, and line segments have a length, which is equal to the distance between its endpoints. Houses are like points, a path is like a line segment.
26.) You have SO many examples of midpoint in your notes by now! Find the distance between the two points. Find half of that distance. REMEMBER THAT HALF THE DISTANCE IS NOT THE SAME THING AS THE MIDPOINT! Use half of the distance to find the location of the midpoint, by adding it to the starting point or subtracting it from the endpoint. That value is your midpoint.
27.) Create a diagram, then label the diagram with the info given and create a true equation. (4x does not equal 5x+2, CD+DE=CE)
28.) Draw segment AB and then put C somewhere on it. Label the diagram with the info given and create a true equation. (Between does not mean middle, x+3 does not equal 8x-2! You have to add things and set them equal to something else)
29.) Draw a right angle (90 degrees) Label it EDF. Remember, bisect means to cut in half. What is half of 90 degrees?
30.) Draw angle ABD first. Then, where does point C need to be so that ABD and DBC are adjacent? Once you have a good diagram, label it with the given information and create a true equation representing what’s given. Solve the equation, but then go back and make sure you answer the question that was actually asked.
31.) Look in your notes for an example of complementary!
32.) What two things add up to equal 180? Show that in an equation! Solve the equation, but then go back and make sure you answer the question that was actually asked.
Answers: 1.) 3 2.) -3 3.) 3 4.) -3 5.) -11
6.) x=18 7.) y=-16 8.) m=-20 9.) z=15
10.) x=0 11.) x=-7 (I skipped 12.) 13.) x=3
14-25.) See image below
26.) Midpoint is 6 27.) DE=12 28.) 9+x+3=8x-2, x=2, so AB=14
29.) Angle EDQ=45 degrees 30.) Angle ABD=36 degrees
31.) angle 2= 73 degrees 32.) Angle NMO=57 degrees