{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-12-06T05:10:45+00:00","modifiedTime":"2016-12-06T05:10:45+00:00","timestamp":"2022-09-14T18:16:40+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"},"slug":"geometry","categoryId":33725}],"title":"How to Copy a Triangle Using a Compass","strippedTitle":"how to copy a triangle using a compass","slug":"copy-triangle-using-compass","canonicalUrl":"","seo":{"metaDescription":"When you copy a triangle, the idea is to use your compass to “measure” the lengths of the three sides of the given triangle and then make another triangle with ","noIndex":0,"noFollow":0},"content":"When you copy a triangle, the idea is to use your compass to “measure” the lengths of the three sides of the given triangle and then make another triangle with sides congruent to the sides of the original triangle.\r\n\r\nThe fact that this method works is related to the SSS method of proving triangles congruent.\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/GEOM-3E_0047_01.gif\"><img class=\"aligncenter wp-image-229930 size-full\" src=\"https://www.dummies.com/wp-content/uploads/GEOM-3E_0047_01.gif\" alt=\"geometry-congruent\" width=\"179\" height=\"43\" /></a>\r\nHere is the proof diagram.\r\n\r\n[caption id=\"attachment_229614\" align=\"aligncenter\" width=\"485\"]<a href=\"https://www.dummies.com/wp-content/uploads/9781119181552-fg2009-REV.gif\"><img class=\"wp-image-229614 size-full\" src=\"https://www.dummies.com/wp-content/uploads/9781119181552-fg2009-REV.gif\" alt=\"geometry-triangle-compass\" width=\"485\" height=\"424\" /></a> Copying a triangle.[/caption]\r\n\r\nAs you work through the following steps, refer to the figure:\r\n<ol>\r\n\t<li><strong>Draw a working line, <em>l,</em> with a point <em>J</em> on it.</strong></li>\r\n\t<li><strong>Put your compass point on point <em>D</em> and open it to the length of <em>DE</em>.</strong>\r\nThe best way to make sure you’ve opened it to just the right amount is to draw a little arc that passes through <em>E</em>. In other words, draw arc (<em>D</em>, <em>DE</em>).</li>\r\n\t<li><strong>Being careful not to change the amount of the compass’s opening from Step 2, put the compass point on point <em>J</em> and construct arc (<em>J</em>, <em>JK</em>) intersecting line <em>l</em>.</strong>\r\nYou have now constructed segment <em>JK</em> on line <em>l</em> that’s congruent to segment <em>DE.</em></li>\r\n\t<li><strong>Construct\r\n</strong>\r\na. Arc (<em>D</em>, <em>DF</em>)\r\nb. Arc (<em>J</em>, <em>DF</em>)</li>\r\n\t<li><strong>Construct\r\n</strong>\r\na. Arc (<em>E</em>, <em>EF</em>)\r\nb. Arc (<em>K</em>, <em>EF</em>) intersecting arc (<em>J</em>, <em>DF</em>) at point <em>L</em></li>\r\n\t<li><strong>Draw segments <em>JL</em> and <em>KL</em> and you’re done.</strong></li>\r\n</ol>","description":"When you copy a triangle, the idea is to use your compass to “measure” the lengths of the three sides of the given triangle and then make another triangle with sides congruent to the sides of the original triangle.\r\n\r\nThe fact that this method works is related to the SSS method of proving triangles congruent.\r\n\r\n<a href=\"https://www.dummies.com/wp-content/uploads/GEOM-3E_0047_01.gif\"><img class=\"aligncenter wp-image-229930 size-full\" src=\"https://www.dummies.com/wp-content/uploads/GEOM-3E_0047_01.gif\" alt=\"geometry-congruent\" width=\"179\" height=\"43\" /></a>\r\nHere is the proof diagram.\r\n\r\n[caption id=\"attachment_229614\" align=\"aligncenter\" width=\"485\"]<a href=\"https://www.dummies.com/wp-content/uploads/9781119181552-fg2009-REV.gif\"><img class=\"wp-image-229614 size-full\" src=\"https://www.dummies.com/wp-content/uploads/9781119181552-fg2009-REV.gif\" alt=\"geometry-triangle-compass\" width=\"485\" height=\"424\" /></a> Copying a triangle.[/caption]\r\n\r\nAs you work through the following steps, refer to the figure:\r\n<ol>\r\n\t<li><strong>Draw a working line, <em>l,</em> with a point <em>J</em> on it.</strong></li>\r\n\t<li><strong>Put your compass point on point <em>D</em> and open it to the length of <em>DE</em>.</strong>\r\nThe best way to make sure you’ve opened it to just the right amount is to draw a little arc that passes through <em>E</em>. In other words, draw arc (<em>D</em>, <em>DE</em>).</li>\r\n\t<li><strong>Being careful not to change the amount of the compass’s opening from Step 2, put the compass point on point <em>J</em> and construct arc (<em>J</em>, <em>JK</em>) intersecting line <em>l</em>.</strong>\r\nYou have now constructed segment <em>JK</em> on line <em>l</em> that’s congruent to segment <em>DE.</em></li>\r\n\t<li><strong>Construct\r\n</strong>\r\na. Arc (<em>D</em>, <em>DF</em>)\r\nb. Arc (<em>J</em>, <em>DF</em>)</li>\r\n\t<li><strong>Construct\r\n</strong>\r\na. Arc (<em>E</em>, <em>EF</em>)\r\nb. Arc (<em>K</em>, <em>EF</em>) intersecting arc (<em>J</em>, <em>DF</em>) at point <em>L</em></li>\r\n\t<li><strong>Draw segments <em>JL</em> and <em>KL</em> and you’re done.</strong></li>\r\n</ol>","blurb":"","authors":[{"authorId":8957,"name":"Mark Ryan","slug":"mark-ryan","description":" <p><b>Mark Ryan</b> has taught pre-algebra through calculus for more than 25 years. In 1997, he founded The Math Center in Winnetka, Illinois, where he teaches junior high and high school mathematics courses as well as standardized test prep classes. He also does extensive one-on-one tutoring. He is a member of the Authors Guild and the National Council of Teachers of Mathematics. 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How to Copy a Triangle Using a Compass

By: Mark Ryan and

Updated: 12-06-2016

From The Book: Geometry For Dummies

Geometry For Dummies

Book image

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When you copy a triangle, the idea is to use your compass to “measure” the lengths of the three sides of the given triangle and then make another triangle with sides congruent to the sides of the original triangle.

The fact that this method works is related to the SSS method of proving triangles congruent.

Here is the proof diagram.

geometry-triangle-compass

Copying a triangle.

As you work through the following steps, refer to the figure:

Draw a working line, l, with a point J on it.
Put your compass point on point D and open it to the length of DE. The best way to make sure you’ve opened it to just the right amount is to draw a little arc that passes through E. In other words, draw arc (D, DE).
Being careful not to change the amount of the compass’s opening from Step 2, put the compass point on point J and construct arc (J, JK) intersecting line l. You have now constructed segment JK on line l that’s congruent to segment DE.
Construct a. Arc (D, DF) b. Arc (J, DF)
Construct a. Arc (E, EF) b. Arc (K, EF) intersecting arc (J, DF) at point L
Draw segments JL and KL and you’re done.

About This Article

This article is from the book:

Geometry For Dummies ,

About the book author:

Mark Ryan is the founder and owner of The Math Center in the Chicago area, where he provides tutoring in all math subjects as well as test preparation. Mark is the author of Calculus For Dummies, Calculus Workbook For Dummies, and Geometry Workbook For Dummies.

This article can be found in the category:

Geometry ,