1. Geometric Conclusions
Determine if each statement is a SOMETIMES, ALWAYS, or NEVER

2. Who Am I? My total angle measure is 360˚.
All of my sides are different lengths.
I have no right angles.

3. Who Am I? I have no right angles My total angle measure is not 360˚
I have fewer than 3 congruent sides.

4. Who Am I? My total angle measure is 360˚ or less.
I have at least one right angle.
I have more than one pair of congruent sides.

5. Who Am I? I have at least one pair of parallel sides.
My total angle measure is 360˚.
No side is perpendicular to any other side.

6. Types of curves
simple curves: A curve is simple if it does not cross itself.

7. Types of Curves
closed curves: a closed curve is a curve with no endpoints and which completely encloses an area

8. Types of Curves
convex curve: If a plane closed curve be such that a straight line can cut it in at most two points, it is called a convex curve.
Convex Curves
Not Convex Curves

9. Triangle Discoveries
Work with a part to see what discoveries can you make about triangles.

10. Types of Triangles Classified by Angles
Equiangular: all angles congruent
Acute: all angles acute
Obtuse: one obtuse angle
Right: one right angle
Classified by Sides
Equilateral: all sides congruent
Isosceles: at least two sides congruent
Scalene: no sides congruent

11. Triangles Scalene (No sides equal)
Isosceles (at least two sides equal)
Equilateral (all sides equal)

12. What’s possible? Equilateral Isosceles Scalene Equiangular Acute Right
Obtuse NO NO NO

13. Homework
Textbook pages
#9-12, #23-26, #49-52

14. Pythagorean Theorem c2 a2 b2
a2 + b2 = c2

15. Pythagorean Theorem

16. Pythagorean Theorem

17. Pythagorean Theorem

18. Pythagorean Theorem

19. Testing for acute, obtuse, right
a2 + b2 = c2
Pythagorean theorem says:
What happens if or
a2 + b2 > c2
a2 + b2 < c2

20. Testing for acute, obtuse, right
Right triangle:
Acute triangle:
Obtuse triangle:
a2 + b2 = c2
a2 + b2 > c2
a2 + b2 < c2

21. Types of Angles Website www.mrperezonlinemathtutor.com Complementary
Supplementary
Adjacent
Vertical

22. Transversals

24. Let’s check the homework!
Textbook pages
#9-12, #23-26, #49-52

25. What is the value of x?
2x + 5
3x + 10

26. Angles in pattern blocks

27. Diagonals
Joining two nonadjacent vertices of a polygon

28. For which shapes will the diagonals always be perpendicular?
Type of Quadrilateral
Are diagonals perpendicular?
Trapezoid
Parallelogram
Rhombus
Rectangle
Square
Kite

29. For which shapes will the diagonals always be perpendicular?
Type of Quadrilateral
Are diagonals perpendicular?
Trapezoid
maybe
Parallelogram
Rhombus
Rectangle
Square
Kite

30. For which shapes will the diagonals always be perpendicular?
Type of Quadrilateral
Are diagonals perpendicular?
Trapezoid
maybe
Parallelogram
Rhombus
Rectangle
Square
Kite

31. For which shapes will the diagonals always be perpendicular?
Type of Quadrilateral
Are diagonals perpendicular?
Trapezoid
maybe
Parallelogram
Rhombus
yes
Rectangle
Square
Kite

32. For which shapes will the diagonals always be perpendicular?
Type of Quadrilateral
Are diagonals perpendicular?
Trapezoid
maybe
Parallelogram
Rhombus
yes
Rectangle
Square
Kite

33. For which shapes will the diagonals always be perpendicular?
Type of Quadrilateral
Are diagonals perpendicular?
Trapezoid
maybe
Parallelogram
Rhombus
yes
Rectangle
Square
Kite

34. For which shapes will the diagonals always be perpendicular?
Type of Quadrilateral
Are diagonals perpendicular?
Trapezoid
maybe
Parallelogram
Rhombus
yes
Rectangle
Square
Kite

35. If m<A = 140°, what is the m<B, m<C and m<D?

36. If m<D = 75°, what is the m<B, m<C and m<A?

37. Sum of the angles of a polygon
Use a minimum of five polygon pieces to create a 5-sided, 6-sided, 7 sided, 8-sided, 9-sided, 10-sided, 11-sided, or 12-sided figure. Trace on triangle grid paper, cut out, mark and measure the total angles in the figure. 2 1 3 4 9 8 2 5 7 1 3 6 4 7 5 6

38. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Undecagon 11
Dodecagon 12
Triskaidecagon 13
Nth N
What patterns do you see?

39. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Undecagon 11
Dodecagon 12
Triskaidecagon 13
nth n
What patterns do you see?

40. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
360
Pentagon 5
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Undecagon 11
Dodecagon 12
Triskaidecagon 13
nth n
What patterns do you see?

41. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
360
Pentagon 5
540
Hexagon 6
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Undecagon 11
Dodecagon 12
Triskaidecagon 13
nth n
What patterns do you see?

42. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
360
Pentagon 5
540
Hexagon 6
720
Heptagon 7
Octagon 8
Nonagon 9
Decagon 10
Undecagon 11
Dodecagon 12
Triskaidecagon 13
nth n
What patterns do you see?

43. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
360
Pentagon 5
540
Hexagon 6
720
Heptagon 7
900
Octagon 8
Nonagon 9
Decagon 10
Undecagon 11
Dodecagon 12
Triskaidecagon 13
nth n
What patterns do you see?

44. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
360
Pentagon 5
540
Hexagon 6
720
Heptagon 7
900
Octagon 8
1080
Nonagon 9
Decagon 10
Undecagon 11
Dodecagon 12
Triskaidecagon 13
nth n
What patterns do you see?

45. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
360
Pentagon 5
540
Hexagon 6
720
Heptagon 7
900
Octagon 8
1080
Nonagon 9
1260
Decagon 10
Undecagon 11
Dodecagon 12
Triskaidecagon 13
nth n
What patterns do you see?

46. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
360
Pentagon 5
540
Hexagon 6
720
Heptagon 7
900
Octagon 8
1080
Nonagon 9
1260
Decagon 10
1440
Undecagon 11
Dodecagon 12
Triskaidecagon 13
nth n
What patterns do you see?

47. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
360
Pentagon 5
540
Hexagon 6
720
Heptagon 7
900
Octagon 8
1080
Nonagon 9
1260
Decagon 10
1440
Undecagon 11
1620
Dodecagon 12
Triskaidecagon 13
nth n
What patterns do you see?

48. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
360
Pentagon 5
540
Hexagon 6
720
Heptagon 7
900
Octagon 8
1080
Nonagon 9
1260
Decagon 10
1440
Undecagon 11
1620
Dodecagon 12
1800
Triskaidecagon 13
nth n
What patterns do you see?

49. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
360
Pentagon 5
540
Hexagon 6
720
Heptagon 7
900
Octagon 8
1080
Nonagon 9
1260
Decagon 10
1440
Undecagon 11
1620
Dodecagon 12
1800
Triskaidecagon 13
1980
nth n
What patterns do you see?

50. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
360
Pentagon 5
540
Hexagon 6
720
Heptagon 7
900
Octagon 8
1080
Nonagon 9
1260
Decagon 10
1440
Undecagon 11
1620
Dodecagon 12
1800
Triskaidecagon 13
1980
nth n ?
What patterns do you see?

51. Sum of the angles of a polygon
# sides
Total degrees
Triangle 3
180
Quadrilateral 4
360
Pentagon 5
540
Hexagon 6
720
Heptagon 7
900
Octagon 8
1080
Nonagon 9
1260
Decagon 10
1440
Undecagon 11
1620
Dodecagon 12
1800
Triskaidecagon 13
1980
nth n
180(n-2)
What patterns do you see?

52. Total degree of angles in polygon

53. Area Ideas
Triangles
Parallelograms
Trapezoids
Irregular figures

54. Area Formulas: Triangle

55. Area Formulas: Triangle
1. Using a ruler, draw a diagonal (from one corner to the opposite corner) on shapes A, B, and C.
2. Along the top edge of shape D, mark a point that is not a vertex. Using a ruler, draw a line from each bottom corner to the point you marked. (Three triangles should be formed.)
3. Cut out the shapes. Then, divide A, B, and C into two parts by cutting along the diagonal, and divide D into three parts by cutting along the lines you drew.
4. How do the areas of the resulting shapes compare to the area of the original shape?

56. Area Formulas: Triangle

57. Area Formulas: Triangle

58. Area Formulas: Trapezoids

59. Area Formulas: Trapezoids
Do you have suggestions for finding area?
What other shapes could you use to help you?
Are there any other shapes for which you already know how to find the area?

60. Area Formulas: Trapezoids
18cm
15 cm
13 cm
11cm
24 cm

61. Connect Math Shapes Set
CMP Cuisenaire® Connected Math Shapes Set (1 set of 206) ISBN-10: X ISBN-13: Price: $29.35

62. Area Formulas: Trapezoids
A = ½h(b1 + b2)
When triangles are removed from each corner and rotated, a rectangle will be formed. It’s important for kids to see that the midline is equal to the average of the bases. This is the basis for the proof—the midline is equal to the base of the newly formed rectangle, and the midline can be expressed as ½(b1 + b2), so the proof falls immediately into place. To be sure that students see this relationship, ask, "How is the midline related to the two bases?" Students might suggest that the length of the midline is "exactly between" the lengths of the two bases; more precisely, some students may indicate that it is equal to the average of the two bases, giving the necessary expression.
Remind students that the area of a rectangle is base × height; for the rectangle formed from the original trapezoid, the base is ½(b1 + b2) and the height is h, so the area of the rectangle (and, consequently, of the trapezoid) is A = ½h(b1 + b2). This is the traditional formula for finding the area of the trapezoid.

63. Area Formulas: Trapezoids
18cm
15 cm
13 cm
11cm
24 cm

64. Area Formulas: Trapezoids
Websites:

65. Parallelograms

66. A = Length x width

67. Area of Parallelogram
Can you estimate the area of Tennessee?

68. Area of irregular figure?

69. Find the area of the irregular figure.

70. Area of irregular figure?

71. Area of irregular figure?

72. Fact: m<1 = 30˚ and m<7 = 100 ˚
Find:
m<2
m<3
m<4
m<5
m<6
m<8
m<9
m<10
m<11
m<12 5 6 8 7 2 10 4 9 1 12 3 11

73. Fact: m<1 = 30˚ and m<7 = 100 ˚5
80 ˚ 6
80 ˚ 8 7
100 ˚
130 ˚
150 ˚
50 ˚ 10 4
30˚ 9 2 1 11 12 3
30˚
50 ˚
130 ˚
150 ˚
m<1 + m<5 + m<12 = _______
m<2 + m<8 + m<11 = _______

74. The sum of which 3 angles will equal 180˚?2 3 1 4 8 9 10 5 11 12 7 6

75. The sum of which 3 angles will equal 360˚?2 3 1 4 8 9 10 5 11 12 7 6

76. Pentominos
How many ways can you arrange five tiles with at least one edge touching another edge?
Use your tiles to determine arrangements and cut out each from graph paper.

77. Pentominos

78. Archimedes’ Puzzle 1 8 2 4 9 3 10 12 13 7 6 11 5 14