1. Properties of Triangles and Quadrilateral
Chapter 8
Properties of Triangles and Quadrilateral
02/2017
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2. 8-1A: Points, Lines, and Planes
I can… Identify and label basic geometric figures.
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3. Vocabulary:
Point: a point has no dimension. It is represented by a dot.
Line: A line has one dimension. Through any two points, there is exactly one line. A B l A

4. Rays and line segments are parts of lines.
A ___________ has a definite beginning and end.
line segment
A line segment is part of a line containing two endpoints
and all points between them.
A line segment is named using
its endpoints.
The line segment is named
segment AB or segment BA
The symbol for segment AB is A B

5. Rays and line segments are parts of lines.
A ___ has a definite starting point and extends
without end in one direction.
ray A B
RAY:
The starting point of a ray is called the ________.
endpoint
A ray is named using the endpoint first, then another point on the ray.
The ray above is named ray AB.
The symbol for ray AB is

6. Use three points to name a plane.B A C
Plane: a plane has two dimensions. It is represented by a shape that looks like piece of paper, but extends without end.
Use three points to name a plane.

7. Lines:
Intersecting lines Perpendicular Lines Parallel Lines
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8. Congruent:
Same shape and size
Symbol:
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9. Identify the figures: F
1) 4) 2) 5) 3) P A X F N M E C D
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10. 12/10/2018
Homework:
p. 443 #1 - 25
02/2017
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11. 8-1B: Measuring Angles
I can…
measure and classify angles.
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12. There is another case where two rays can have a common endpoint.
This figure is called an _____.
angle S
Some parts of angles have
special names.
side
The common endpoint is
called the ______,
vertex R T
side
vertex
and the two rays that make
up the sides of the angle are
called the sides of the angle.

13. You can use a _________ to measure angles and
sketch angles of given measure.
protractor
1) Place the center point of the protractor on vertex R. Align the straightedge with side RS. Q R S
Use the scale that begins
with 0 at RS. Read where the
other side of the angle, RQ,
crosses this scale.

14. Once the measure of an angle is known, the angle can
be classified as one of three types of angles. These
types are defined in relation to a right angle.
Types of Angles A A A
obtuse angle 90 < m A < 180
right angle m A = 90
acute angle 0 < m A < 90

15. Classify each angle as acute, obtuse, or right.
110°
90°
40°
Obtuse
Right
Acute
75°
50°
130°
Acute
Obtuse
Acute

16. 12/10/2018
Homework:
p. 448 #1 - 27
02/2017
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17. 8-1C: Angle Relationships
I can…
classify and apply angle relationships
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18. When two lines intersect, ____ angles are formed. four
There are two pairs of angles across from each other.
These pairs are called _____________.
vertical angles
Vertical angles are congruent! 1 4 2 3
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19. Supplementary angles:
Two angles whose sum is 180o
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20. Complementary Angles:
Two angles whose sum is 90o
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21. Example: Classify the angles as complementary, supplementary, or neither
1) 3) 2)
60º
120º
60º
40º
60º
30º
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22. Find the missing angles.
1) )
83º ?º
62º ?º
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23. Find the missing angles.
25o yo xo
30o
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24. 12/10/2018
Homework:
p. 454 #9 - 35
02/2017
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25. 8-2B: Triangles
I can…
classify triangles and find missing angles measures in triangles
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26. Triangle:
A figure with three sides and three angles. The sum of its angles is always 180 degrees.
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27. Triangles Classified by Angles acute triangle obtuse triangle right
60°
80°
17°
43°
30°
60°
120°
40°
1 obtuse angle, 2 acute
1 right angle, 2 acute
All angles are acute

28. Triangles
Classified by
Sides
scalene
isosceles
equilateral
___
sides
congruent no
__________
sides
congruent
at least two
___
sides
congruent
all

29. Example: 1) Draw a right isosceles triangle.
2) Draw an acute scalene triangle.
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30. Example: Find the missing angle.
35o
65o
12/10/2018
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31. Find the missing angle.
370 x
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32. 12/10/2018
Homework:
Workbook p. 127
02/2017
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33. Chapter 8 Midchapter Test
12/10/2018
Chapter 8 Midchapter Test
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34. 8-3B: Properties of Quadrilaterals
I can… classify quadrilaterals and find missing angles measures in quadrilaterals.
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35. Graphic organizer
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36. 12/10/2018
Homework:
Workbook p. 131
02/2017
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37. 8-3C: Properties of Polygons
I can… classify polygons and find the sum of angle measures in a polygon.
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38. Polygons
The word polygon means “many angles”
A two dimensional object
A closed figure

39. More about Polygons
Made up of three or more straight line segments
There are exactly two sides that meet at a vertex
The sides do not cross each other

40. Examples of Polygons

41. These are not Polygons

42. Interior angle: An angle on the inside of the polygon.

43. Diagonals and Angle Measure Number of Diagonals from One Vertex
Make a table like the one below.
1) Draw a convex quadrilateral.
2) Choose one vertex and draw all possible diagonals from that vertex.
3) How many triangles are formed?
Convex
Polygon
Number
of Sides
Number of Diagonals from One Vertex
Number of
Triangles
Sum of
Interior Angles
quadrilateral 4 1 2
2(180) = 360

44. Diagonals and Angle Measure Number of Diagonals from One Vertex
1) Draw a convex pentagon.
2) Choose one vertex and draw all
possible diagonals from that vertex.
3) How many triangles are formed?
Convex
Polygon
Number
of Sides
Number of Diagonals from One Vertex
Number of
Triangles
Sum of
Interior Angles
quadrilateral 4 1 2
2(180) = 360
pentagon 5 2 3
3(180) = 540

45. Diagonals and Angle Measure Number of Diagonals from One Vertex
1) Draw a convex hexagon.
2) Choose one vertex and draw all
possible diagonals from that vertex.
3) How many triangles are formed?
Convex
Polygon
Number
of Sides
Number of Diagonals from One Vertex
Number of
Triangles
Sum of
Interior Angles
quadrilateral 4 1 2
2(180) = 360
pentagon 5 2 3
3(180) = 540
hexagon 6 3 4
4(180) = 720

46. Diagonals and Angle Measure Number of Diagonals from One Vertex
1) Draw a convex heptagon.
2) Choose one vertex and draw all
possible diagonals from that vertex.
3) How many triangles are formed?
Convex
Polygon
Number
of Sides
Number of Diagonals from One Vertex
Number of
Triangles
Sum of
Interior Angles
quadrilateral 4 1 2
2(180) = 360
pentagon 5 2 3
3(180) = 540
hexagon 6 3 4
4(180) = 720
heptagon 7 4 5
5(180) = 900

47. Diagonals and Angle Measure Number of Diagonals from One Vertex
1) Any convex polygon.
2) All possible diagonals from one vertex.
3) How many triangles?
Convex
Polygon
Number
of Sides
Number of Diagonals from One Vertex
Number of
Triangles
Sum of
Interior Angles
quadrilateral 4 1 2
2(180) = 360
pentagon 5 2 3
3(180) = 540
hexagon 6 3 4
4(180) = 720
heptagon 7 4 5
5(180) = 900
n-gon n
n - 3
n - 2
(n – 2)180

48. Find the measure of the interior angles of the regular octogon.

49. 12/10/2018
Homework:
p. 477 #7-25odd, 34 – 37all
02/2017
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50. 8-3D: Similar and Congruent Figures
I can… identify similar and congruent figures.
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51. Congruent Figures: figures with the same size and shape.
Similar Figures: figures with the same shape, but can be different sizes; all angles are congruent
Congruent Figures: figures with the same size and shape.
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52. 1. Which of these shapes are congruent to the yellow one?4 3 2 5 7 8 6

53. Congruent shapes are all shown in yellow – were you right?1 4 3 2 5 7 8 6

54. Similar shapes

55. Which of these shapes are similar to the yellow one?1 4 3 2 5 7 8 6

56. Similar shapes are all shown in yellow – were you right?
Start page
Similar shapes are all shown in yellow – were you right? 1 4 3 2 5 7 8 6

57. Corresponding sides: sides of similar or congruent figures that are in the same relative position.
6/20/2011
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58. 12/10/2018
Homework:
p.483 #1 – 23 odd, 29
02/2017
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59. Coordinate Plane Basics
I can… draw a coordinate plane, label quadrants, and plot ordered pairs.
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60. 12/10/2018
Homework:
worksheets
02/2017
LSowatsky

61. 8-4B: Translations I can… graph translations on a coordinate plane.
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62. 12/10/2018
Homework:
Workbook p. 137
02/2017
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63. 8-4C: Reflections I can… graph reflections on a coordinate plane.
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64. 12/10/2018
Homework:
Workbook p. 139
02/2017
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65. 8-4D: Rotations I can… graph rotations on a coordinate plane.
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66. 12/10/2018
Homework:
Workbook p. 141
02/2017
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67. 12/10/2018
Chapter 8 Test
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