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Definition
| Simply write the name of the letter that appears next to the dot that represents the point, like this: A. |
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Pick any two points the line (only two!). Write the names of the points next to each other and draw a double-headed arrow over the top of them.
Here's an example:
[image] |
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| How do you name a line segment? |
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Definition
Pick the points where the segment starts and ends. Write the names of the points next to each other and draw a stroke across the top of them without arrowheads. Here's an example:
[image] |
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What is the difference between the following two sets of symbols:
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Definition
| The first one is the name of the line segment that starts at point H and ends at point P. The second represents the length of that line segment. |
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Definition
| "the length of line segment PQ" or "the measure of line segment PQ" |
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Definition
Pick the end point of the ray (which is really where they ray starts!) and any one other point on the ray. Write the names of the points next to each other, starting with the endpoint, and draw a one-headed arrow with the arrowhead toward the right. This shows that the ray starts at the first point and continues in the direction of the second point. Here's an example:
[image] |
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Term
| How do you name an angle. |
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Definition
Use the angle's vertex and then pick one point from each of the rays that form the angle.
Now draw an angle symbol and write the names of the points next to each other after the angle symbol with the name of the vertex in the middle, like this: LAVB |
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Definition
| "the measure of angle A, V, B" |
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Definition
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Term
| What difference between the following two sets of symbols LAVB and mLAVB? |
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Definition
| They first is the name of the angle whose vertex is V and whose sides are ray VA and ray VB. The second represents the angle's measure. |
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Term
Name the line segment that starts at O and ends at C two different ways.
[image] |
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Definition
[image]
The order of the points doesn't matter when naming a line segment. |
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Name the line that passes through (or contains) points O, C and D in at least four ways.
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Definition
There are 12 possibilities:
[image]
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Name the ray that starts at B and proceeds in the direction of O two different ways.
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Definition
These are the only two possible names:
[image]
Remember, the "endpoint" must be listed first, and the one-headed arrow must point to the right. |
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Term
Name the angle whose vertex is O and whose interior contains I in three different ways.
[image] |
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Definition
| There are four possibilities: LEOC, LEOD, LCOE, LDOE |
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Term
Do LBOC and LBCO name the same angle? Why or why not?
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Definition
| No, the vertex of the angle is always the middle point named. The vertex of the first angle is O and the vertex of the second angle is C. |
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Term
Do LBOC and LBOD name the same angle? Why or why not?
[image]
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Definition
Yes, the angles share the same vertex and the same sides.
The sides of LBOC are ray OB and ray OC. The sides of LBOC are ray OB and OD. Ray OC and ray OD are named differently, but they are the same ray. |
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Term
Do these two sets of symbols name the same ray? Why or why not?
[image]
[image] |
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Definition
| No, although they share the same "endpoint," they proceed in opposite directions. |
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Term
Do these two sets of symbols name the same ray? Why or why not?
[image]
[image] |
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Definition
| Yes, because they start at the same point and proceed in the same direction. Points C and D are both in the same direction from point O. Remember also that ray OC doesn't stop at point C, it continues on forever in the direction of C. |
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Term
| What does the reflexive property say? |
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Definition
| A thing is equal to itself: a = a. |
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Term
| What does the symmetric property say? |
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Definition
Equations are true forward and backward:
If a = b, then b = a. |
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Term
| What does the transitive property say? |
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Definition
If two things are equal to the same thing, then they are equal to each other:
If a = c, and b = c, then a = b.
a and b are both equal to c. So they are equal to each other. |
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| What does the substitution property say? |
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Definition
If two things are equal to each other, then they can replace each other in true equations, and the equations will remain true.
Example:
If 2a + 7 = b and a = 3b +5 then 2(3b+5) + 7 = b.
We replaced a in the first equation with 3b + 5. We can do that because a = 3b + 5. |
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| What does the addition property say? |
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Definition
If equals are added to equals, then the sums are equal:
If a = b, then a + c = b + c. |
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| What does the subtraction property say? |
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Definition
If equals are subtracted from equals, then the differences are equal:
If a = b, then a - c = b - c. |
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Term
| What does the multiplication property say? |
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Definition
If equals are multiplied by equals, then the products are equal:
If a = b, then ac = bc. |
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Term
| What does the division property say? |
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Definition
If equals are divided by equals, then the quotients are equal:
If a = b, then a/c = b/c. |
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Term
Name the property illustrated:
3x + 7 = 3x + 7 |
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Definition
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Term
Name the property illustrated:
19 - n = 7. So 7 = 19 - n |
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Definition
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Name the property illustrated:
3x + 5 = 17 and 2y - 5 = 17. So 3x + 5 = 2y - 5. |
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Definition
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Term
Name the property illustrated:
y = 3x - 19 and x = 3y So y = 3(3y) - 19. |
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Definition
| the substitution property |
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Term
Name the property illustrated:
3x - 23 = 157. So 3x -23 + 23 = 157 + 23 |
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Definition
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Name the property illustrated:
95 = 48 + 5y So 95 - 48 = 48 + 5y - 48. |
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Definition
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Name the property illustrated:
98 = m/13 So 13(98) = 13(m/13) |
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Definition
| the multiplication property |
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Term
Name the property illustrated:
17z = 289 So (17z)/17 = 289/17 |
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Definition
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