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Lesson 1.1Patterns and
Inductive ReasoningYou will learn to…* find and describe patterns* use inductive reasoning to make conjectures
Describe the pattern.Find the next three numbers.
3. 0, 1, 1, 2, 3, 5, 8,…
4. 4, 9, 16, 25, …
5. 1 2 3 4 2 3 4 5
13, 21, 34
36, 49, 64
__ , __ , __ , __ , 5 6 76 7 8
__ , __ , __
Complete the conjecture.8. The sum of any 2 odd
numbers is __________.even
odd9. The product of any 2 odd numbers is __________.
Find a counterexample.
10. The sum of 2 numbers is always greater than the larger of the numbers.
11. If a shape has 2 sides the same length, then it must be a rectangle.
Describe the pattern. Find the next numbers or letters in the sequence.
12.
13. 14. A, 2, B, 0, C, 2, D, 0, E, 3,…
J, F, M, A, …
O, T, T, F, …
F, 3, G, 2, H, 4, …
M, J, J, A, S, O , N, D
F, S, S, E, N, T, …
Lesson 1.2Points, Lines,
and PlanesYou will learn to…* understand and use the basic
geometry terms* sketch intersections of lines and planes
Collinear points
Coplanar points
Coplanar lines
A BC
AB
C
points that lie on the same line
points that lie in the same plane
lines that lie in the same plane
Lesson 1.3Segments & Their
MeasuresYou will learn to…* use segment postulates* use the distance formula
The distance between points A and B is written as AB which is the length of AB.
-3 -2 -1 0 1 2 3
A B
AB = | - 2 – 3| or | 3 – - 2| = 5
Distance is the absolute value of their difference.
A postulate is a statement or rule that is accepted
without proof.
Rules that are proven are called theorems.
9. Suppose M is between L and N. Use the Segment Addition Postulate to solve for x.
5x + 3 = 233x + 8 + 2x – 5 = 23
LM = 3x + 8MN = 2x – 5LN = 23
5x = 20x = 4
ML N
10. E is between H and R. A is between E and R. R is between E and T. HT = 50, ER = 20, and HE=EA=AR. Find RT.
EA = AR =
H E A R T
50
20
10
1010
HE = 10
10
RT = 20
12. Use the Pythagorean Theorem to find the distance between the points.
(1,2)
(4,6)
3
4c2= 32 + 42
c2= 9 + 16
c2= 25c= 5
(4-1)2 + (6-2)2?
(x2-x1)2 + (y2-y1)2
Distance Formula
If A (x1, y1) and B (x2, y2) are points in a coordinate plane, then
AB = (x2 – x1)2 + (y2 – y1)2
13. Find TM T (3, -2) and M (1, 4)
TM = (1 - 3)2 + (4 - -2)2
TM = (-2)2 + (6)2
TM = 4 + 36 = 40 ≈ 6.324 · 10 = 2 10
Lesson 1.4Angles and Their
MeasuresYou will learn to…* use angle postulates* classify angles as acute, right, obtuse, or straight
An angle consists of 2 rays that have the same endpoint
called the vertex of the angle.
YX and YZ form XYZ
X
Y
Z
60°
Two angles are Adjacent Angles if they share a vertex and a side
but have no common interior points.
A
B
C
D
ABC and CBD are
adjacent angles
(not overlapping)
How do you measure an angle with a protractor?
5. Use a protractor to draw a 65˚ angle.
6. Use a protractor to draw a 112˚ angle.
A midpoint is a point that divides a segment into two
congruent segments.
midpoint
A B
M
AM = MB
AM MB
To bisect a segment means to divide it into two congruent segments.
Use a compass to locate the midpoint of a segment.
How would you find the “middle” between
2 numbers?
How would you find the “middle” between
the points?
3. One endpoint is (-3, -1). The midpoint is (3, -4). Find the other endpoint.
(-3,-1), (3,-4), (x , y) -3 + x
2
= 3 -1 + y 2 = -4
-3 + x = 6 -1 + y = -8x = 9 y = -7
31
-4 1
(9, -7)
3. One endpoint is (3, -5). The midpoint is (-2, 4). Find the other endpoint.
(3,-5), (-2,4), (x , y)
3 + x = -4 -5 + y = 8x = -7 y = 13
(-7,13) 3 + x
2= -2 -5 + y
2 = 4
7. BD bisects ABC. m ABD = (2x + 50)˚ m DBC = (5x + 5)˚ Find the measure of all 3 angles.
DA
CB
80°
x = 15 80°
mABC =
5x+5 = 2x+50
3x = 45
160°
Lesson 1.6Angle Pair
RelationshipsYou will learn to…* identify vertical angles and linear pairs* identify complementary and supplementary angles
2
A 180˚ angle forms a straight angle.
Two angles are Supplementary Angles
if the sum of their measures is 180
Two angles are vertical angles if they are NOT adjacent and their sides are formed
by 2 intersecting lines.
21
34
vertical angles
1 and 2 3 and 4
Two angles form a linear pair
if they are adjacent angles whose noncommon sides
form a line.
21
34 1 and 4
2 and 4
linear pairs
1 and 3
2 and 3
5. Find x and y. Then find the angle measures.
(4x + 15)° (3y + 15)°
(3y - 15)°(5x + 30)°
5x+30+4x+15=180
y = 30
105°
105°75°
75°
x = 15
3y-15+3y+15=180
1. Find the area of a square that has a side length of 20 inches.
Find the perimeter.
A = 202
A = 400 inches2
P = 4(20)P = 80 inches
2. Find the area of a rectangle that is 20 m by 4 m. Find the perimeter.
A = 20(4)A = 80 m2
P = 2(20) + 2(4)P = 48 m
3. A rectangle has an area of 98 cm2. Find the length of its base if its height is 7 cm.
A = b(h)98 = b(7)b = 14 cm
Find the area and perimeter of the triangle.4.
16 cm
9 cm15 cm
9(16) 2A = = 72 cm2
P = 40.8 cm
9.8 cm
c2 = 42 + 92
124152 = x2 + 92
5. Find the area and perimeter of the triangle.
9 cm
10 cm6 cm
A = 9(6) 2
A = 27 cm2
?
c2 = 92 + 102
13.5
c2 = 92 + 42
?9.8
P = 29.3 cm
Find the area of the triangle.
6.
20 cm
12 cm
25 cm 20(15) 2 A=
A = 150 cm2
Pythagorean Theorem?
15 cm
7. Find the circumference.
8. Find the circumference.
6 cm
C = 37.7cm
C =10 cm
31.4 cm
12π cm ≈
10π cm ≈
2π 2π
9. Find the radius of the circle that has a circumference of 120 feet.
120 = 2rπ
19.1≈ r
C = dπ C = 2rπ C = 2rπ
12. Find the radius of the circle that has
an area of 120 square feet.120 = r2 π
r ≈ 6.2 ft
π π
r2 = 38.197
r = 38.197
13. Find the perimeter and area of the triangle.
AC = 6
AB =
BC =
34 ≈ 5.8
34 ≈ 5.8
P = 6 + 2 34 ≈ 17.6
A = ½ (5)(6) =(-2,-4)
A(3,-1)B
(-2,2)C
height = 5
15 square units
AB = (-2 - 3)2 + (-4 - -1)2BC = (3 --2)2 + (-1 - 2)2
14. Find the area of the bluish region.
Square - Circle = 144 - 36π ≈ 30.9 cm2
Square?
12 cm Circle?A = 62 π = 36π
A = 122 = 144
15. Find the area of the bluish region. r = 5
Square - Circles = 400 – 4(25π) ≈ 85.84
Square?
Circle?A = 52 π = 25π
A = 202 = 400