1. Chapter 1: Basics of Geometry

2. 1-1: Patterns and Inductive Reasoning

3. conjecture
an unproven statement that is based on observations

4. a process that includes looking for patterns and making conjectures
inductive reasoning
a process that includes looking for patterns and making conjectures

5. Conjecture Information
To prove a conjecture is true, you need to prove it is true in ALL cases.
To prove a conjecture is false, provide a single counterexample.
Conjectures that are not known to be true or false are called unproven or undecided.

6. counterexample
an example that shows a conjecture is false

7. Let’s Go on To the Next Section! 

8. 1-2: Points, Lines, and Planes

9. Today’s Objectives name points, lines, segments, rays and planes
name a point that is collinear with given points
name a point that is coplanar with given points

10. definition
uses known words to describe a new word

11. undefined terms
a word that is not formally defined (point, line, plane) although there is general agreement about what the word means

12. point a point has no dimension and is represented by a small dot ●A

13. line
a line extends in one dimension and is usually represented by a straight line with two arrowheads to indicate that the line extends without end in two directions
● ● A B AB or BA

14. Facts About Lines
is designated by 2 capital letters which represent two points on the line
may also be designated by a small letter that labels the whole line
is understood to be straight unless stated otherwise
is the shortest distance between two points

15. plane
a collection of points that forms a flat surface infinitely wide and infinitely long
plane M

16. collinear points points that lie on the same line
segments and rays are collinear if they lie on the same line

17. coplanar points points that lie on the same plane
segments, rays, and lines are coplanar if they lie on the same plane

18. line segment/segment
part of a line that consists of two endpoints and all points on the line that are between the endpoints
● ● A B AB or BA

19. endpoints points at either end of a segment
name segments using the endpoints

20. ray
part of a line that consists of an initial point and all points on the line that extend in one direction
● ● B A BA only

21. initial point the point at the beginning of a ray
when naming rays, start with the initial point

22. Question
Describe what each of these symbols means: PQ QP

23. opposite rays
if C is between A and B, then ray CA and ray CB are opposite rays
● ● ● A C B

24. Question Name two pairs of opposite rays in the figure.
● ● ● ● E F G H

25. intersect
to have one or more points in common
● A

26. intersection
the set of points that two or more geometric figures have in common

27. Question
How can lines intersect at more than one point?

28. Question
When you see a dashed line in a diagram, what does that usually imply?

29. Skill 1-2a
I will name points, lines, segments, rays and planes.

30. Number 1a ●B

31. Number 2a

32. Number 3a

33. Number 4a

34. Number 5a

35. Skill 1-2b
I will name a point that is collinear with given points.

36. Number 1b
point D

37. Number 2b
point H

38. Number 3b
point G

39. Number 4b
Points C and Q

40. Number 5b
Points P and R

41. Number 6b
Points A and Q

42. Skill 1-2c
I will name a point that is coplanar with given points.

43. Number 1c
point D

44. Number 2c
point H

45. Number 3c
Points D, E, and H

46. Number 4c
Points E, F, and G

47. Number 5c
Points G, H, and A

48. Let’s Do Some Homework! 

49. 1-3: Segments and Their Measures

50. Today’s Objectives use the segment addition postulate correctly
use the distance formula to measure distances

51. postulates/axioms
rules that are accepted without proof

52. Postulate 1— Ruler Postulate
The points on a line can be matched one to one with the real numbers (coordinate).

53. length of a segment
the distance between the endpoints of a segment

54. Postulate 2—Segment Addition Postulate
If B is between A and C, then AB + BC = AC.
If AB + BC = AC, then B is between A and C.

55. Question
Draw a sketch of three collinear points. Label them. Then write the Segment Addition Postulate for the points.

56. Question
A car with a trailer has a total length of 27 feet. If the trailer has a total length of 13 feet, how long is the car?

57. Distance Formula
If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the distance between A and B is

58. The Distance Formula “On Top of Old Smokey”
When finding the distance between two points subtract the two x’s. Do the same for the y’s. Now square both these numbers, and find out their sum. When you take the square root, then you are all done!

59. congruent segments
segments that have the same length

60. Question
Explain the difference between the terms equal and congruent.

61. Skill 1-3a
I will use the segment addition postulate correctly.

62. Number 1a
Find XY

63. Number 2a
Find MN

64. Number 3a
Find MO

65. Number 4a Points A, D, F, and X are on a segment in this order.
AD = 15, AF = 22, and AX = 30.
Find DF and FX.

66. Skill 1-3b
I will use the distance formula to measure distances.

67. Number 1b
C(0, 0) and D(5, 2)

68. Number 2b
G(3, 0) and H(8, 10)

69. Number 3b
V(-2, -6) and W(1, -2)

70. Let’s Do Some Homework! 

71. 1-4: Angles and Their Measures

72. Today’s Objectives measure angles using a protractor
use angle addition postulates correctly
classify angles as acute, right, obtuse, or straight
find the intersection and union of geometric figures

73. angle
consists of two different rays that have the same initial point
vertex ● side

74. sides of an angle
the rays that make up an angle

75. vertex of an angle the initial point of the angle
or where B is the vertex and are the sides

76. Naming an Angle
Use three letters. The center letter corresponds to the vertex.
Place a number or letter at the vertex in the interior of the angle. This may be used only if there is one angle at the vertex.

77. Question
Name the vertex of angle XYZ.

78. congruent angles
angles that have the same measure

79. measure of an angle
the size of the opening of the angle measured in degrees

80. Postulate 3—Protractor Postulate
Consider a point A on one side of The rays of the form can be matched one to one with the real numbers from 0 to 180.
●A ● ● O B

81. interior of an angle
all points between the points that lie on each side of the angle
interior

82. exterior of an angle all points not on the angle or in its interior
exterior exterior

83. Postulate 4—Angle Addition Postulate
If P is in the interior of , then
R● S● P● T●

84. Question
How are the Segment Addition Postulate and the Angle Addition Postulate similar?

85. Question
How are the Segment Addition Postulate and the Angle Addition Postulate different?

86. acute angle
an angle with measure between 0° and 90°

87. right angle
an angle with measure equal to 90°

88. obtuse angle
an angle with measure between 90° and 180°

89. straight angle
an angle with measure equal to 180°

90. reflex angle
an angle with measure greater than 180° and less than 360°

91. adjacent angles
two angles with a common vertex and side but no common interior points
1 2

92. Question
Name the angles in the figure.
M N O
● ● ● ●P

93. Intersection and Union
An intersection of two sets A and B is the set consisting of all the members that belong to both sets A and B.
Look to see what is in common
A union of two sets A and B is the set consisting of all members belonging to at least one of the sets A and B.
Put the sets together

94. Skill 1-4a
I will measure angles using a protractor.

95. Number 1a

96. Number 2a

97. Number 3a

98. Number 4a

99. Skill 1-4b
I will use angle addition postulates correctly.

100. Number 1b

101. Number 2b
mLAOB = 37° and mLBOC = 24°
Find mLAOC

102. Number 3b
mLAOB = 46° and mLAOC = 84°
Find mLBOC

103. Skill 1-4c
I will classify angles as acute, right, obtuse, or straight.

104. Number 1c

105. Number 2c

106. Number 3c

107. Skill 1-4d
I will find the intersection and union of geometric figures.

108. Number 1d

109. Number 2d

110. Number 3d

111. Number 4d

112. Let’s Do Some Homework! 

113. 1-5: Segment and Angle Bisectors

114. Today’s Objectives use construction tools to bisect a segment
find the midpoint or endpoint of a segment using the midpoint formula
use construction tools to bisect an angle
find angle measures after an angle has been bisected

115. midpoint
the point that divides, or bisects, a segment into two congruent segments

116. bisects
to divide into two congruent parts
● l ● l ●

117. Question
How do you indicate congruent segments in a diagram?

118. segment bisector
a segment, ray, line, or plane that intersects a segment at its midpoint
● l ● l ●

119. bisecting a segment do a compass and straightedge construction
use paper folding
use the midpoint formula

120. compass
a construction tool used to draw arcs

121. straightedge
a construction tool used to draw segments usually a ruler without marks

122. construction
a geometric drawing that uses a limited set of tools, usually a compass and a straightedge

123. Constructing a Segment Bisector
You are given a segment with endpoints AB.
Place the compass point at point A.
Use a compass setting greater than half the length of segment AB.
Draw an arc.

124. Keep the same compass setting.
Place the compass point at B.
Draw an arc that should intersect the other arc in two places above and below the segment.
Use a straightedge to draw a segment through the points of intersection.

125. Midpoint Formula
If A(x1, y1) and B(x2, y2) are points in a coordinate plane, then the midpoint of has coordinates

126. The Midpoint Formula “The Itsy Bitsy Spider”
 When finding the midpoint of two points on a graph,
Add the two x’s and cut their sum in half.
Add up the y’s and divide ‘em by a two.
Now write ‘em as an ordered pair.
You’ve got the middle of the two.

127. angle bisector
a ray that divides an angle into two adjacent angles that are congruent

128. Question
How do you indicate congruent angles in a diagram?

129. Constructing an Angle Bisector
You are given angle C.
Place the compass point at C.
Draw an arc that intersects both sides of the angle.
Label the intersections A and B.
Place the compass point at A.
Draw an arc.

130. Then place the compass point at B.
Using the same compass setting, draw another arc.
Label the intersection D.
Use a straightedge to draw a ray through C and D.

131. Skill 1-5a
I will use construction tools to bisect a segment.

132. Number 1a

133. Number 2a

134. Skill 1-5b
I will find the midpoint or endpoint of a segment using the midpoint formula.

135. Number 1b
endpoints D(3, 5) and E(-4, 0)

136. Number 2b
Endpoints A(-2, 3) and B(5, -2)

137. Number 3b
M(3, -4) one endpoint of XY is Y(-3, -1)

138. Number 4b
M(2, 4) one endpoint of RP is R(-1, 7)

139. Skill 1-5c
I will use construction tools to bisect an angle.

140. Number 1c

141. Number 2c

142. Skill 1-5d
I will find angle measures after an angle has been bisected.

143. Number 1d

144. Number 2d

145. Number 3d

146. Number 4d

147. Let’s Do Some Homework! 

148. 1-6: Angle Pair Relationships

149. Today’s Objectives
identify and find values for vertical angles and linear pairs
identify and find values for complementary and supplementary angles

150. vertical angles two angles whose sides form two pairs of opposite rays
1 angles 1 & angles 2 &

151. linear pair
two adjacent angles whose non-common sides are opposite rays
5 6 angles 5 & 6

152. two angles whose measures have the sum 90°
complementary angles
two angles whose measures have the sum 90°
can be adjacent or non-adjacent

153. complement
the sum of the measures of an angle and its complement is 90°

154. supplementary angles
two angles whose measures have the sum 180°
can be adjacent or non-adjacent

155. supplement
the sum of the measures of an angle and its supplement is 180°

156. Question
The angles in a linear pair are always _____.

157. Question
Explain the difference between complementary angles and supplementary angles.

158. Skill 1-6a
I will identify and find values for vertical angles and linear pairs.

159. Number 1a
Name all of the vertical angles.

160. Number 2a
Name all of the linear pairs.

161. Number 3a
Solve for x.

162. Number 4a
Solve for each angle.

163. Skill 1-6b
I will identify and find values for complementary and supplementary angles.

164. Number 1b
Two supplementary angles have measures of (4x + 15)° and (5x + 30).° Find x.

165. Number 2b
Given that angle U is a complement of angle V, and the measure of angle U is 73°, find

166. Number 3b
Solve for each angle.

167. Let’s Do Some Homework! 

168. 1-7: Introduction to Perimeter, Circumference, and Area

169. Today’s Objectives
find the perimeter and area of common plane figures

170. Perimeter
abbreviated P
the distance around a figure
measured in units

171. Circumference abbreviated C the perimeter of a circle
measured in units

172. Area
abbreviated A
the space inside a figure
measured in units2

173. Formulas for a Square
side length s
P = 4s
A = s2

174. Formulas for a Rectangle
length l and width w
P = 2l + 2w OR P = 2(l + w)
A = lw

175. Formulas for a Triangle
side lengths a, b, and c
P = a + b + c
base b
height h (forms a right angle with the base)
A = ½bh

176. Formulas for a Circle radius r = ½d diameter d = 2r C = 2 r or d
A = r2
is approximately 3.14

177. Pythagorean Theorem a2 + b2 = c2 only works for right triangles
a and b are legs
c is the hypotenuse
this is the longest side
located across from the right angle

178. Question
What do you call the perimeter of a circle?

179. Question
Explain how to find the circumference and area of a circle if you know its diameter.

180. Question
What is the difference between the area and perimeter of a figure?

181. Skill 1-7
I will find the perimeter and area of common plane figures.

182. Number 1
The perimeter of a square is 12 meters. What is the length of a side of the square?

183. Number 2
You are putting a fence around a rectangular garden with length 15 feet and width 8 feet. What is the length of the fence that you will need?

184. Number 3
Find the area and circumference.

185. Number 4
Find the area and perimeter.

186. Number 5
Find the area and perimeter.

187. Let’s Do Some Homework! 