These ancient tools, and others similar to them, are the early versions of the modern technology used today for designing and measuring. They were designed and then constructed using tools that are similar to today’s protractor, compass and Mira. Think of some famous ancient structures such as pyramids, coliseums and cathedrals. Be ready to share some real-world examples of how angles are used that your students will find interesting and relatable.)Īll the major human-built historical masterpiece were built with great precision by following detailed design plans. If available, have a Mira for each student, too, although they are not required to complete the worksheet. Make copies of the Angles and Reflections Worksheet and have a supply of protractors for students to individually use. (Have handy a protractor and Mira ready to demonstrate to the class. Students should know that the reflection of a line always has equal angles, that a straight line is 180° and that a right angle is 90°. Explain how engineers use geometry tools to design everyday products and infrastructure.Īngles and Reflections Worksheet Answer Key (pdf) Visit [ to print or download.Ī familiarity with angles-what they are, how they are identified and characterized, and examples of how they are used in action sports, architecture, navigation, etc.Describe how to reflect points and lines using a geometry tool.Use geometric tools to measure and draw angles.is the same as 30° in China.Īfter this lesson, students should be able to: These tools also help us communicate across different spoken languages and cultures since they are universal-that is, 30° in the U.S. Engineers rely on their tools to provide consistent ways of measuring, especially aspects such as length and angles, to enable modern feats of engineering from skyscrapers to satellites. Today, the same tools are used by engineers for creating precise design drawings for modern infrastructure, systems and products. Over time, these tools became more complex and enabled more accuracy and greater design precision. This lesson prepares students to conduct the associated activity in which they “solve the holes” for hole-in-one multiple-banked angle solutions, make their own one-hole mini-golf courses with their own geometry-based problems and solutions, and then compare their “on paper” solutions to real-world results.Īncient Egyptian and Roman engineers used geometry tools to create impressive structures and sites that still stand today. Through the lesson, students gain an awareness of the pervasive use of angles, and these tools, for design purposes related to engineering and everyday uses. After seeing some class practice problems and completing a set of worksheet-prompted problems, students share their methods and work. The lesson begins with a recap of the history and modern-day use of protractors, compasses and mirrors. Students learn about common geometry tools and then learn to use protractors (and Miras, if available) to create and measure angles and reflections.
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