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# Similar Triangles in Mapping (TR2): HSG.MG.A.1

Common Core Standards
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2 MB|9 pages
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Students will use similar triangles to model geographic relationships, connecting data from the real world to a map. Students will interpret the resulting triangles on the map and draw conclusions. The Take-home Message: If two pairs of angles in two triangles are congruent, the triangles are similar and the sides are proportional. After finding two different bearings to an object in the real world, and knowing the distance between the points from which we took the bearings, we can make a map or locate the object, by drawing a triangle which is similar to the triangle measured in the real world. This mission is aligned with Common Core State Standards: HSG.MG.A.1.

The fun stuff:
How did people make accurate maps before GPS? While GPS can tell us our location, how can we determine the location of an object we see in the distance? A map is a 2-D scale model of the real-world, and triangles on the map are similar to their real-world counterparts. With simple tools and measurements, we can determine the location of a distant fire or mountain! Great applications of similarity, angle measurement and proportions!

The zip file includes:
★The mission. (6 pages).
★A two-page Quick Start guide for teachers. Detailed and helpful!

The mission includes:
•Drawing rays representing different bearings.
•Determining angles between bearings.
•Using bearings to sketch triangles and locate objects.
•Using bearings to create a simple map.
•Writing and solving proportions to determine distances.

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Total Pages
9 pages
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Teaching Duration
1 hour
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