1. Geometry

2. Chapter 9
Material

3. Basic Terms
Point
Segment
Line
Ray
Angle

4. Angle Terms Vertex Sides Names Measures: Decimal Degrees
Degrees, Minutes, Seconds A V B

5. Angle Measure Convert 32.5˚ to D˚M’S”. Convert 95.265˚ to D˚M’S”.
A full revolution is _____ degrees.

6. Types of Angles Acute (< 90˚) Right (= 90˚) Obtuse (> 90˚)
Straight (= 180˚)

7. Line Relationships
Intersecting
Perpendicular
Parallel
Skew

8. Angle Relationships Adjacent Vertical Complementary (sum is 90˚)
Supplementary (sum is 180˚)
137˚
48˚

9. Transversal Angles Interior/Exterior
Alternate interior/ alternate exterior
Corresponding
Same side interior/ same side exterior
75˚

10. Polygons A simple closed figure made of line segments
A regular polygon has all sides equal in length and all angles equal in measure.

11. Types of Polygons 3 Triangle 9 Nonagon 4 Quadrilateral 10 Decagon
5 Pentagon 11 Undecagon
6 Hexagon 12 Dodecagon
7 Heptagon N N-gon
8 Octagon

12. Types of Triangles
Triangles are classified according to relationships between sides:
Scalene
Isosceles
Equilateral

13. Types of Triangles Triangles are also classified according to angles:
Acute
Equiangular
Right
Obtuse

14. Triangle Fact
The measures of the interior angles of any triangle add to _____ degrees.
78˚
40˚

15. Types of Quadrilaterals
Parallelogram
Rectangle
Rhombus
Square
Kite
Trapezoid
Isosceles Trapezoid

16. Quadrilateral Fact
The measures of the interior angles of any quadrilateral add to _____ degrees.
68˚
65˚

17. Other Polygons: Angle Sum
We can generalize on the sum of the measures of the interior angles of any polygon.
Find the sum of the interior angles in a:
dodecagon

18. Another Interesting Fact: The sum of the measures of the exterior angles of any polygon is always _______ degrees.
Find the measure of each interior angle of a regular dodecagon

19. Diagonals Line segments connecting non-consecutive vertices
General formula:

20. Three-Dimensional Shapes

21. Three-Dimensional Shapes
5 Platonic solids: Made completely with congruent regular polygons
Tetrahedron
Hexahedron
Octahedron
Dodecahedron
Icosahedron

22. Three-Dimensional Shapes
Drawing in 3-D “1101”
Cube
Prism: Rectangular and Triangular
Pyramid: Square and Triangular
Circular Cylinder
Circular Cone
Sphere

23. Chapter 11
Material

24. Metric Measurement Prefix Chart: Roots: Length ― meter (m)
T G M k h dk ROOT d c m µ n p
Roots: Length ― meter (m)
Capacity ― liter (L)
Mass ― gram (g)

25. Customary Measurement
Length facts:
12 in. = 1 ft
3 ft = 1 yd
36 in. = 1 yd
1760 yd = 1 mi
5280 ft = 1 mi
Mass facts:
16 oz = 1 lb
2000 lb = 1 T
Capacity facts:
4 qt = 1 gal

26. Temperature Conversions

27. Perimeter
The perimeter of any triangle (or any other type of polygon) is the sum of the measures of the lengths of its sides.
5 ft
30 m
3 ft
4 ft
Assume this is a regular hexagon.

28. Area of a Triangle The common area formula is
Find the area of each triangle.
11.5 cm
16.8 cm
12 ft
9 ft

29. Quadrilaterals: Area & Perimeter
Square: A = P = 4b
Rhombus: A = bh P = 4b
Parallelogram: A = bh P = 2(a + b)
Rectangle: A = bh P = 2(b + h)
Trapezoid: A = P = a + b + c + d

30. Quadrilaterals: Area & Perimeter
Find the area and perimeter of each figure.
20 ft
10 ft
8 ft
90 ft
Assume this is a square.
7.65 m
5.4 m

31. Quadrilaterals: Area & Perimeter
A rectangular field has dimensions 275 ft by 145 ft. If fence costs $1.79 per running foot, find the total cost of fencing the field.
If a bag of seed costs $10.95 and covers an average of 5,000 square feet, find the total cost of seeding this field.

32. Area of a Regular Polygon
General formula:
a = length of apothem
n = # of sides
s = length of a side a s

33. Circle Circumference The distance around the circle Formulas:
C = 2 π r
C = π d d r
r = radius, d = diameter, π = pi (a number close to )

34. Circle Circumference
The earth has a radius of approximately 3,960 miles. Find the distance around the earth along the equator.
A bicycle tire has a diameter of 26 inches. Find how far the bike travels in 1 full revolution of the tire.

35. Circle Area A measure of the size of the region inside the circle
Formulas:
r = d ∕ 2 r d

36. Circle Area
You measure a circle’s diameter to be 5 feet. Find the circle’s area.
If the area of a circle is 250 square meters, find the radius of the circle.

37. The Pythagorean Theorem
The sum of the squares of the lengths of the legs of a right triangle equals the square of the length of the hypotenuse. c a b

38. The Pythagorean Theorem
Do the following represent lengths of sides of a right triangle?
6 cm, 8 cm, 10 cm
10 ft, 10 ft, 20 ft
4 mi, 5 mi, 7 mi
7 in., 24 in., 25 in.

39. The Pythagorean Theorem
Find the missing lengths.
75 ft
11.5 cm
16.8 cm
93 yd
67 yd

40. Three-Dimensional Shapes

41. Rectangular Prism Volume: V = l w h
Surface Area: A = 2 l w + 2 w h + 2 l h
l = length
w = width
h = height h w l

42. Rectangular Prism
Find the volume and surface area of the following room.
24 ft
8 ft
18 ft

43. Right Circular Cylinder
Volume: a measure of space inside a 3-dimensional shape r h

44. Right Circular Cylinder
Find the volume if r = 24 m and h = 40 m.
Find the diameter of a cylindrical tank 15 ft high with a capacity of 136,000 gallons. (1 cubic foot holds approximately 7.48 gallons)

45. Right Circular Cylinder
Surface area:
Find the lateral (L) and total (T) surface areas if r = 5 feet and h = 9 feet.

46. Challenge!
Orient an 8.5” by 11” piece of paper vertically and horizontally, folding to make a right circular cylinder. Compare volumes, lateral surface areas, and total surface areas.
Which is greater ― the circumference of a tennis can lid or the height of the tennis can?

47. Sphere Volume: Surface Area:
The earth has a radius of approximately 3,960 miles. Find the surface area and volume of the earth.

48. Geometry is all around us!