1. Friday, February 22, 2019Friday, February 22, 2019
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2. Segments, Angles and intersections
Review Naming
3-D drawing
Collinear and Coplanar
Intersections
Segment Addition
Angle Addition
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3. Review Naming stuff Lines: pick 2 points and draw a line over ‘em A B
Segments: draw a segment over the endpoints X Y Z
Rays: endpoint first, then any other point.
Draw a ray above ‘em R S T
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4. Basic 3-D Geometry
What is the geometric name for the BLUE flat surface?
A flat surface is called a plane.
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5. Basic 3-D Geometry How many planes are pictured here?
There are 2 planes the green one and the blue one.
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6. Basic 3-D Geometry What do the dotted lines mean?
They are the “hidden” lines, or the ones you can’t see.
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7. Basic 3-D Geometry
If this object was in your back yard, this is how it would look.
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8. Basic 3-D Geometry Friday, February 22, 2019Friday, February 22, 2019
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9. Basic 3-D Geometry Friday, February 22, 2019Friday, February 22, 2019
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10. Basic 3-D Geometry Friday, February 22, 2019Friday, February 22, 2019
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11. Collinear & Coplanar Notes Collinear Points on the same line A B C
Points A, B and C are collinear
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12. Collinear & Coplanar Notes Collinear Points on the same line Z Y X
Points X, Y and Z are collinear
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13. Collinear & Coplanar Notes Collinear Points on the same line
Points R, S and T
Are NOT collinear T S R
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14. Collinear & Coplanar Notes 2 Points Are always collinear N M
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15. Collinear & Coplanar Notes Coplanar Points in the same plane
Three points are always coplanar
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16. Basic 3-D Geometry Points A, B and C are coplanar B A C
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17. Basic 3-D Geometry Points A, B and C are coplanar B C A
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18. Basic 3-D Geometry Points A, B, C and D are NOT coplanar D B C A
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19. Review VOCAB Coplanar: on the same plane Q R L T S
S,T,L and Q are coplanar
R,S,T and Q are NOT coplanar
3 points are always coplanar
Friday, February 22, 2019Friday, February 22, 2019
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20. Basic 3-D Geometry A B What is the name for this line?
Normally, we would name it with 2 points.
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21. Basic 3-D Geometry “Intersection” is where two objects “touch”
What “shape” do the two planes make where they intersect?
A Line.
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22. Basic 3-D Geometry But this line has no points!
So we put its name in the picture
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23. Review VOCAB Collinear: on the same line T R S
R, S and T are collinear L
L, M and N are
NOT collinear N M
2 points are always collinear
Friday, February 22, 2019Friday, February 22, 2019
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24. Review Intersections POINT
When lines intersect, they intersect at a ___________.
LINE
When planes intersect, they intersect at a ___________.
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25. Naming angles Name a point on one side of the angle. Name the Vertex.
Name a point on the other side of the angle.
Possible names: A B C
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26. Supplements First, you have to know what a LINEAR PAIR is
Adjacent: Next to. (For angles, it means sharing a side and vertex)
These are not adjacent
These are adjacent
A LINEAR PAIR are adjacent angles that make a straight line.
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27. Supplements Supplements are any 2 angles whose measures add to 1800
But they do not have to be linear pair
170+10=180
170 10
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28. Compliments Compliments are any 2 angles whose measures add to 900
But they do not have to be adjacent
80+10=90 80 10
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29. Vertical Angles If we move the Scissors so the red angle gets bigger,
What will happen
To the yellow angle?
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30. Vertical Angles If we move the Scissors so the red angle gets bigger,
What will happen
To the yellow angle?
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31. Vertical Angles If we move the Scissors so the red angle gets bigger,
What will happen
To the yellow angle?
Friday, February 22, 2019Friday, February 22, 2019
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32. Vertical Angles If we move the Scissors so the red angle gets bigger,
What will happen
To the yellow angle?
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33. Vertical Angles EVERY TIME you see this picture…
1. Any angles next to each other
add to 180
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34. Vertical Angles EVERY TIME you see this picture…
1. Any angles next to each other
add to 180
Angles across from each other
are equal
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35. Vertical Angles EVERY TIME you see this picture…
1. Any angles next to each other
add to 180 60
Angles across from each other
are equal
120
120 60
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36. Vertical Angles EVERY TIME you see this picture…
1. Any angles next to each other
add to 180 80
Angles across from each other
are equal
100
100 80
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37. SAMPLE PROBLEMS 50 110 1. What is the compliment of 400?
2. What is the supplement of 700?
110
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38. SAMPLE PROBLEMS 140 + x = 180 30 + x = 90 X = 60 X = 40 3. Find X
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39. Vertical Angles Find X, Y and Z 75 X 105 105 Z Y 75
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40. Quiz tomorrow: 40 35 8 15 (it will be multiple choice, four questions)
BC is the angle bisector. #1
k is the segment bisector. #2 A C
x + 20 35 5x 40 B D k 40 35
5X =
X + 20 = 8 15
X =
X =
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41. Segment addition postulate
If B is between A and C then AC = AB + BC
In other words . . . A C 10 B 20
Then AC = ?
= 30
Friday, February 22, 2019
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42. Segment addition postulate
CONGRUENT
Objects that are the same size and shape. (Geometry’s version of equals) D 7 C A 7 B
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43. Segment addition postulate
Sample problem: Find XZ X Y Z
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44. ANGLES A B C
VERTEX
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45. ANGLES A NAMING Start with a point on one side Then the vertex B
Then a point on the other side C
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46. ANGLES TYPES: ACUTE OBTUSE RIGHT STRAIGHT Less than 90 More than 90 90
180
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47. ANGLES Angle addition postulate: A X B C Friday, February 22, 2019
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48. ANGLES Sample problem: find A X B C Friday, February 22, 2019
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