1. Tennessee Adult Education Mathematics Curriculum 2011
Pre-GED
Geometry
Lesson 7

2. What is Geometry?
It is the branch of mathematics that deals with lines, points, curves, angles, surfaces, and solids.

3. Lines - Basic Terms Term Definition Point (•)
A location on an object or a position in space.
Line
A connected set of points that extends without end in two directions.
Line Segment
A piece of a line, like a jump rope, that is a specific length.
Ray
Part of a line that extends indefinitely in one direction.

4. Naming Lines Lines are named by the points that are located on them.
Example:
This line can be named in 2 ways: AB or BA A B
This reads “line AB”
Line segments are named by the points that are located on them.
Example:
This line segment can be named in 2 ways: CD or DC C D
This reads “line segment CD”

5. Naming Rays Rays are named by the points that are located on them.
Example: F E EF
There is only one way to name a ray.
The end point must go first!
This reads “ray EF”

6. Guided Practice Directions: Name the figures. 2. _______ 1. _______ CB D A E
3. _______ F

7. Guided Practice Directions: Name the figures. CD or DC AB BA
2. _______
1. _______ or C B D A E EF
3. _______ F

8. Lines that form a right angle when they intersect
Term
Definition
Parallel Lines
Lines that are always the same distance apart from each other. They will never intersect.
Perpendicular Lines
Lines that form a right angle when they intersect
Intersecting Lines
Lines that cross, or that will cross. The point at which they cross is called the vertex.
Transversal Lines
is a line that intersects a set of parallel lines.

9. Naming Parallel Lines
When naming parallel lines, first name the lines, then place the symbol for parallel in the middle.
Symbol for parallel: II R S RS II TU T U
This reads “ line RS is parallel to line TU”

10. Naming Perpendicular Lines
When naming perpendicular lines, first name the lines, then place the symbol for perpendicular in the middle.
Symbol for perpendicular: R RS TU T U S
This reads “ line RS is perpendicular to line TU”

11. Guided Practice
Directions: Tell whether each figure is perpendicular or parallel, then name the lines. U Q S W X R T V
1. _____________________
2. _____________________

12. Guided Practice
Directions: Tell whether each figure is perpendicular or parallel, then name the lines. U Q S W X R T V
parallel
QR II ST
perpendicular
UV WX
1. _____________________
2. _____________________

13. Basic Shapes Polygons Quadrilateral
Are closed flat shapes with 3 or more straight sides.
Quadrilateral
are polygons that have four sides and four angles.
Name
Shape
Triangles
Parallelograms
Quadrilaterals
Rectangles
Pentagon
Square
Hexagon
Rhombus
Octagon
Trapezoid

14. quadrilaterals A four sided figure a b
Parallelogram: has 2 sets of parallel sides. c d
AB ll CD
and
AC ll BD
Rectangle: is a parallelogram, each set of parallel sides must be equal in length, and must form 4 right angles.
The small boxes in the corners indicate a right angle.
Angles will be discussed later in the lesson

15. More quadrilaterals
4 inches
Square: is a parallelogram, all sides are equal in length, and must have 4 right angles
4 inches
4 inches
4 inches
5 inches
5 inches
Rhombus: is a parallelogram, all sides are equal in length, angle measurement does not matter.
5 inches
5 inches A B
Trapezoid: has one set of parallel sides
AB II CD C D
AC is not parallel to BD

16. Guided Practice Directions: Name the Quadrilaterals. 1.
________________
2. ________________
3. _________________
_________________ 2. 3. 4. 5.

17. Guided Practice Directions: Name the Quadrilaterals. 1. Trapezoid
________________
2. ________________
3. _________________
_________________
Parallelogram 2.
Square 3.
Rectangle
Rhombus 4. 5.

18. What are angles?
An angle measures the amount of turn. As the Angle Increases, the Name Changes.
Pictures from clipart

19. Type of Angle Description
Acute
An angle less than 90°
Right
An angle that is 90° exactly
Obtuse
An angle that is more than 90°
Straight
An angle that is exactly 180°
Reflex
An angle that is greater than 180°

20. Parts of an Angle
The point at which the two rays meet is called the vertex.
The two straight sides are called rays.
The angle is the amount of turn between each ray.
Ray
Ray
angle
Vertex

21. Guided Practice
Directions: Classify each angle as acute, right, obtuse, or straight.
1. ___________
2. ___________
3. ___________
4. ___________
5. ___________
6. ___________

22. Guided Practice
Directions: Classify each angle as acute, right, obtuse, or straight.
Obtuse
1. ___________
2. ___________
Right
Acute
3. ___________
Right
Acute
4. ___________
5. ___________
6. ___________
Straight

23. Naming Angles There are three ways to name angles:
Name an angle by the vertex.
For example: B
Name an angle by all three letters.
For example: ABC
CBA
HINT: The vertex is always the middle letter

24. Guided Practice Directions: Name each angle in three ways. _____ G I LJ K H M
_____ N O

25. Guided Practice Directions: Name each angle in three ways. JKL _____
LKJ G I
GHI K
_____ L
IHG J K H H M
MNO
_____ N
ONM O N

26. Supplementary Angles
The two angles below (140⁰ and 40⁰) are supplementary angles, because their measurements add up to 180⁰.
NOTICE: When the two angles are put together, they form a straight line.

27. Complementary Angles
The two angles at the right (40° and 50°) are Complementary Angles, because they add up to 90°.
NOTICE: When the two angles are placed together, they form a corner.

28. Complementary vs Supplementary
How can you remember which is which? Easy! Think:
"C" of Complementary stands for "Corner" (a Right Angle), and
"S" of Supplementary stands for "Straight" (180 degrees is a straight line)

29. Guided Practice
Directions: Find the missing angles using complementary or supplementary rules. 1. 2.
160˚ x x
52˚
x = _________
x = _________ 3. 4. x
43˚ x
100˚
x = _________
x = _________

30. Guided Practice
Directions: Find the missing angles using complementary or supplementary rules. 1. 2. 90
- 52
160˚
180
- 160 x x
52˚ 38
20˚ 20
x = _________
x = _________
38˚ 3. 4. 90
- 43
180
- 100 x
43˚ x
100˚ 47 80
47˚
x = _________
x = _________
80˚

31. a + b + c = 180⁰ What are Triangles?
A triangle has three sides and three angles
The three angles always add to 180° a
a + b + c = 180⁰ b c

32. Triangle Example
Add the two known angles, then subtract the total from 180. x
Step 1:
Step 2: =
160
180
- 160 20
x = 20˚
80˚
80˚
Check:
= 180

33. Guided Practice
Directions: Find the missing angle measurement for each triangle. 1.
60˚
x = _________
x = _________
60˚ x x 3.
20˚
20˚ 2.
20˚
x = _________ x
80˚

34. Guided Practice
Directions: Find the missing angle measurement for each triangle. 1. =
100
60˚
60˚
x = _________ =
120
180
- 100
180
- 120
80˚ 80
x = _________
60˚ x 60 x 3.
20˚
20˚ 2.
20˚
140˚
x = _________ = 40
180
- 40
140 x
80˚

35. Area of a Triangle "b" is the distance along the base of the triangle
"h" is the height (measured at right angles to the base)
Area = base x height 2

36. Example: What is the area of this triangle?
ft.
Hint: The fraction line means divide. Therefore, 240 ÷ 2 =
120
ft.
Every area is expressed in square units

37. Guided Practice Find the area of each triangle
Remember to put the answer in squared units 2. 1.
8 feet
4 feet
7 feet
5 feet 3.
10 inches
2 inches

38. Guided Practice Find the area of each triangle
Remember to put the answer in squared units.
A= b x h 2
A= b x h 2
A = 5 x 8 2 2. 1.
A = 4 x 7 2
A = 40 2
8 feet
4 feet
A = 28 2
7 feet
5 feet 3.
A= b x h 2
A = 2 x 10 2
10 inches
A = 20 2
2 inches

39. Finding the Perimeter 24 in. 10 in. 24 + 24 + 10 + 10 = 68 in.
The perimeter is the distance around a figure such as a square, a rectangle, or a triangle.
To find the perimeter of a figure, you simply add up all the sides.
Example:
24 in.
10 in.
= 68 in.

40. Let’s Practice
How many feet of fencing material will Louise need to surround her garden that measure 20 feet on two sides and 10 feet on the other two sides?

41. Let’s Practice
How many feet of fencing material will Louise need to surround her garden that measure 20 feet on two sides and 10 feet on the other two sides? =
60 Feet

42. More Practice Remember to add ALL sides 1. 5 in. 2. 2 cm. 15 cm.
23 mm. 4.
6 ft. 3.
18 mm.
10 ft.
8 ft.

43. More Practice Remember to add ALL sides 1. 15 cm. 5 in. 2. 2 cm. 2 cm.=
34 cm. =
20 in.
23 mm. 4.
6 ft.
6 ft. 3.
18 mm.
18 mm.
10 ft.
10 ft.
23 mm. =
82 mm.
8 ft. =
40 ft.

44. More Geometry operations and terms!
These will be discussed more in-depth in the next level.
1. Circumference of a circle
2. Area of a circle
3. Transversal Lines
4. X,Y Coordinates

45. Circumference: the perimeter around a circle.
Key terms:
Diameter – is the distance across the circle. The symbol for diameter is “d”.
Radius – All the points on the outside of the circle are equal distances from the center of a circle. The symbol for the radius is “r”.
Note: Diameter = 2(Radius) Or
D=2R

46. How to find the circumference:
28 in

47. Area of a circle
HINT: 6² = 6 x 6
6 in

48. Angles Formed by A Transversal
A transversal line is a line that cuts through a set of parallel lines.
As the transversal cuts through, it forms both Corresponding and Vertical Angles
AB CD
This reads as Line AB is parallel to Line CD.
Corresponding angles have equal measurements, and vertical angles have equal measurements.
Transversal line

49. X, y charts Vocabulary X axis = the horizontal axis ( )
Coordinate Plane
Vocabulary
X axis = the horizontal axis ( )
Y axis = the vertical axis ( )
Coordinates = are a set of points that give a specific location on a map or a chart. (x, y)
For example: ( 2, 4)
The first number is the x. Begin at 0. Since the number is positive move to the right to the 2.
The second number is the y. Start from the 2. Since the number is positive, move up 4. 5 4 (2
, 4) 3 2 -4 1 -5 -3 -2 -1 x 1 2 3 4 5 -1 -2 -3 -4 -5 y