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Name ___________ Geometry 1 Unit 1: Basics of Geometry August Monday Tuesday 4 Wednesday Thursday 5 1st Day of Classes 6 8 7 Freshman First Day 1.1 Patterns and 1.2 Points Lines and Inductive Reasoning Planes 1.3 Segments and Their Measures Homework: Patterns notebook pages 5-6 Page 13 #10-42 even, #44- 47 all Page 21 #20-42 even 15 12 13 Meet Your Teacher 14 11 Review 1.1-1.3 Friday 1.4 Angles and Their 1.4 Angles and Their 1.5 Segment and Measures Measures Using Algebra Review Angle Bisectors Page 8 #34-41 all, page 15 #56-66 Page 30 #26-40 even, page 23 #46- page 29 #1-8 all, #12- even, Page 31 #50- Page 790 #1-34 1st Pages 38-40 #22-30 54 even 22 even 53 all column only. even, #38-48 even 18 19 20 21 22 1.6 Angle Pair Relationships 1.7 Introduction to Perimeter, Circumference, and Area Page 47-48 #8 - 36 even page 49 #48 and 50 Page 55 #10-26 even, Page 57 #4148 all Review Unit 1 Review Unit 1 Geometry 1 Chapter 1 Basics of Geometry Exam STUDY Page 63 #1-22 all 1 1. Create your own pattern using numbers. Describe the rule for your pattern. 2. Create your own pattern using pictures. Describe the rule for your pattern. 2 Geometry 1 1.1 Patterns and Inductive Reasoning Unit 1: Basics of Geometry Example 1 Describe how to sketch the fourth figure in the pattern. Then sketch the fourth figure. Figure 4 ________________________________________________________________________ Figure 5 Example 2 Describe the pattern in the numbers –7, –21, –63, –189,… Write the next three numbers in the pattern Describe the pattern in the numbers 5.01, 5.03, 5.05, 5.07,… Write the next three numbers in the pattern. 3 4 5 1. Write two conjectures that are true. Give examples to support your conjectures. 2. Write 2 conjectures that are false. Write a counterexample for each conjecture. 6 Conjecture Inductive Reasoning Example 3 Number of Points 1 2 3 4 5 Pictures Number of Connections Conjecture: Example 4 Numbers such as 3, 4, and 5 are called consecutive integers. Make and test a conjecture about the sum of any three consecutive integers. Make and test a conjecture about the sign of the product of any three negative integers. Counterexample Example 5 Conjecture: The sum of two numbers is always greater than the larger number. ________________________________________________________________________ Conjecture: The value of x2 is always greater than the value of x. 7 Draw real-life examples of points, lines and planes. 8 Geometry 2 1.2 Points, Line and Planes Unit 1: Basics of Geometry Definition Undefined Terms Building Blocks of Geometry Point Line Plane 9 Activity: Modeling Intersections McDougall Littell Geometry Page 12 10 Collinear Coplanar Line Segment Ray Initial Point Between Opposite Rays 11 Draw a sketch illustrate the meaning of the following statements. The Segment Addition Postulate states that AB + BC = AC if B is between A and C and the points are collinear. If the points are not collinear, then AB + BC > AC. 12 Geometry 1 1.3 Segments and Their Measures Postulates Unit 1: Basics of Geometry Ruler Postulate Segment Length Example 1 Measure the length of the segment to the nearest millimeter D E Between Segment Addition Postulate 13 Use the map to determine the distance from Nico’s to Casa Grande Union High School. Each grid line represents 1/4th a mile. What is the distance “as the crow flies?” 14 Example 2 Two friends leave their homes and walk in a straight line toward the others home. When they meet, one has walked 425 yards and the other has walked 267 yards. How far apart are their homes? The Distance Formula Example 3 Congruent Segment Markings 15 Explain how the distance formula and Pythagorean Theorem are related. Draw a picture to illustrate your thoughts. 16 Distance Formula and the Pythagorean Theorem B(x2, y2) |y2 – y1| A(x1, y1) C(x2, y1) |x2 – x1| c a b Example 4 17 Activity: Geometric Constructions McDougall Littell Geometry Page 25 18 Mixed review Page 24 60-71 all 60. Picture for 68 – 71 61. 68. Picture for 62-67 69. 62. 70. 63. 71. 64. 65. 66. 67. 19 Activity: Paper Folding McDougall Littell Geometry Page 31 #54 20 Geometry 1 1.4 Angles and Their Measures Angle Unit 1: Basics of Geometry Sides Vertex Naming and angle Example 1 D A 1 B C Protractor Things to Know 21 22 Measure of an Angle Congruent Angles Angle measure notation Protractor postulate A O B Step 1 Step 2 Step 3 23 24 Interior Exterior Angle Addition Postulate Example 2 The backyard of a house is illuminated by a light fixture that has two bulbs. Each bulb illuminates an angle of 120°. If the angle illuminated only by the right bulb is 35°, what is the angle illuminated by both bulbs? Acute angle Right angle Obtuse angle 25 What is wrong with this statement? Angles that share a common side are adjacent. Draw a picture of adjacent angles. Draw a picture of angles that share a side but are not adjacent. 26 Straight angle Example 3 Adjacent angles Example 4 27 Activity: Folding Bisectors McDougall Littell Geometry Page 33 28 Mixed Review Page 32 #61-79 61. 65. 62. 66. 63. 67. 64. 68. Picture for 70-73 69. 70. 72. 71. 73. 74. 75. 76. 77. 78. 79. 29 Construction: Segment Bisector and Midpoint McDougall Littell Geometry Page 34 30 Geometry 1 1.5 Segment and Angle Bisectors Midpoint Unit 1: Basics of Geometry Bisect Segment bisector Compass Straightedge Construction Midpoint Formula Example 1 Example 2 31 Construction: Angle Bisector McDougall Littell Geometry Page 36 32 Example 3 Example 4 Angle bisector Example 5 Example 6 Example 7 33 Draw an example of lines adjacent angles that form vertical angles. Draw an example of adjacent angles that do not form vertical angles. 34 Geometry 1 1.6 Angle Pair Relationships Vertical angles Unit 1: Basics of Geometry Linear pair of angles Example 1 2 1 3 5 4 Example 2 35 What is the difference between supplementary angles and a linear pair of angles? Draw examples to illustrate your explanation. 36 Example 3 M (4x + 15)° P (5x + 30)° N (3y + 15)° (3y – 15)° L O Complementary angles Supplementary angles Example 4 Example 5 Example 6 Example 7 37 Use Illustrations to show how the area formulas are related to each other. How is the area of a rectangle use to find the area of a parallelogram, and triangle? How is the formula for a parallelogram used to find the area of a circle? 38 Geometry 1 1.7 Introduction to Perimeter, Circumference, and Area Square Unit 1: Basics of Geometry Rectangle Triangle Circle Example 1 Find the perimeter and area of a rectangle of length 4.5m and width 0.5m. Example 2 A road sign consists of a pole with a circular sign on top. The top of the circle is 10 feet high and the bottom of the circle is 8 feet high. Find the diameter, radius, circumference and area of the circle. Use π ≈ 3.14. 39 40 Example 3 Find the area and perimeter of the triangle defined by H(-2, 2), J(3, -1), and K(-2, -4). Example 4 A maintenance worker needs to fertilize a 9-hole golf course. The entire course covers a rectangular area that is approximately 1800 feet by 2700 feet. Each bag of fertilizer covers 20,000 square feet. How many bags will the worker need? Example 5 You are designing a mat for a picture. The picture is 8 inches wide and 10 inches tall. The mat is to be 2 inches wide. What is the area of the mat? Example 6 You are making a triangular window. The height of the window is 18 inches and the area should be 297 square inches. What should the base of the window be? 41