![]() ![]() The top of this triangle is usually referred to as angle A, written A. Examine the diagram of equilateral ΔABC at right. But in order to clearly describe relationships between angles, you will need a convenient way to refer to and name them. Douglas s reflection trick works, you need to learn more about the relationships between angles. Chapter 2: Angles and Measurement 79Ĥ 2-2. Douglas s trick works? Talk about this with your team and be ready to share your ideas with the class. What appears to be true about the lines of sight? Can you explain why Mr. At right is a diagram of a student trying out the mirror trick. Does the trick work for any angle between the sides of the mirror? Change the angle between the sides of the mirror until you can no longer see your reflection where the sides meet. ![]() Can you see yourself? What if you look in the mirror from a different angle? b. Look into the place where the sides of the mirror meet. By forming a right angle with a hinged mirror, test Mr. He claims that if he makes a right angle with a hinged mirror, he can see himself in the mirror no matter from which direction he looks into it. SOMEBODY S WATCHING ME In order to see yourself in a small mirror, you usually have to be looking directly into it if you move off to the side, you cannot see your image any more. As you examine angle relationships today, keep the following questions in mind to guide your discussion: How can I name the angle? What is the relationship? How do I know? 2-1. ![]() Today you will start by looking at angles to identify relationships in a diagram that make angle measures equal. In this chapter you will examine relationships between parts within a single figure or diagram. For example, two shapes might have sides of the same length or equal angles. 78 Core Connections Geometryģ 2.1.1 What is the relationship? Complementary, Supplementary, and Vertical Angles In Chapter 1, you compared shapes by looking at similarities between their parts. This will allow you to find the perimeter of triangles, parallelograms, and trapezoids, and to find the distance between two points on a graph. Section 2.3 You will review the relationship among the sides of a right triangle called the Pythagorean Theorem. Section 2.2 You will develop methods to find the areas of triangles, parallelograms, and trapezoids as well as more complicated shapes. Section 2.1 You will broaden your understanding of angle to include relationships between angles, such as those formed by intersecting lines or those inside a triangle. How to determine when the lengths of three segments can and cannot form a triangle. The relationship among the three side lengths of a right triangle (the Pythagorean Theorem). How to find the area and perimeter of triangles, parallelograms, and trapezoids. As you work through this chapter, ask yourself: How can I justify my conclusions? The relationships between pairs of angles formed by transversals and the angles in a triangle. In this chapter, you will deepen your understanding of: Angles and Measurement? Mathematically proficient students construct viable arguments and critique the reasoning of others. This will require you to see shapes in multiple ways and to gain a broader understanding of problem solving. Throughout this chapter you will be asked to solve problems, such as those involving area or angles, in more than one way. You will also use transformations from Chapter 1 to uncover special relationships between angles within a figure. In this chapter, you will further investigate how to describe a complex figure by developing ways to accurately determine its angles, area, and perimeter. ![]() 2 CHAPTER 2 In Chapter 1, you studied many common geometric shapes and learned ways to describe a figure using its attributes. ![]()
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