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HL Triangle Congruence

Hypotenuse-leg pairs show right triangle congruence.

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Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

How do we turn a design into reality? In the past, machinists carefully replicated the design using a variety of tools. Today, Computer Numeric Control (CNC) machines and 3D printers produce many of the things we need. These machines use programs to tell them what to do. They take designs made with a Computer-Aided Drafting (CAD) program and turn them into real objects.

Getting It Right

CAD programs have made drafting easier. In the past, technicians had to use rulers, protractors, and other tools to carefully draw a perfect plan. Their work had to be very exact, and if they made a mistake they had to start over. With a CAD program, a drafter can create exact lengths and angles by typing them into the computer. Drafters can use geometry to simplify the design process as well. For instance, if a drafter needed two congruent triangles in his project, he only has to have the computer create two right triangles that have the same hypotenuse and leg—as opposed to inputting all the angle measurements and side lengths of each triangle. Using theorems from geometry like HL triangle congruence can save the drafter time.

Credit: Floyd Ferrel
Source: http://commons.wikimedia.org/wiki/File:Located_at_Chambersburg,_Pennsylvania._A_view_of_a_Computer_Aided_Manufacturing_(CAD-CAM)_system_graphic_terminals_in_use_at_Letterkenny_Army_Depot_DA-SC-84-06770.jpg
License: CC BY-NC 3.0

CAD software is not easy to use. In order to work as a CAD designer, you must complete an associate′s degree. American CAD designers earn a median salary of around $47,800 a year. As CNC machines and 3D printers become more widely used, industries will need more CAD designers to handle drafting and design.

See for yourself: https://www.youtube.com/watch?v=X5AZzOw7FwA

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Are you interested in learning how to use CAD software and designing your own products? You don’t have to wait for graduation. Many cities, schools, libraries, and museums now have “makerspaces,” where teens can use technology to design and create their own items. 




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