Match each step with the correct ordered description for how to construct a copy of an angle.

The constructions associated with copying a segment and copying an angle require that you have a "place" to begin your copy. It is customary to draw a straight line upon which you then produce your copy. Such a line is called a "reference line".

STEPS:
1. Using a straightedge, draw a reference line, if one is not provided.
2. Draw a dot on the reference line to mark your starting point for the construction.
3. Place the point of the compass on point A on the given figure.
4. Stretch the compass so that the pencil is exactly on B. Make a small arc through B.
(This small arc will show that you measured the length of the segment with your compass.)
5. Without changing the span of the compass, place the compass point on the starting point (dot) on the reference line and swing the pencil to create an arc crossing the reference line.
6. Label your copy.

Proof of Construction: The compass was used as a measuring tool to obtain (and copy) the length of the given segment. Since the given segment and the copy are the same length, the segments are congruent.
Note: You may also think of the length from A to B as being the radius of a circle with center at A. By copying the circle at A', the radii segments will be congruent.

STEPS:
1. Using a straightedge, draw a reference line, if one is not provided.
2. Place a dot (starting point) on the reference line.
3. Place the point of the compass on the vertex of the given angle, ∠ABC (vertex at point B).
4. Stretch the compass to any length that will stay "on" the angle.
5. Swing an arc so the pencil will cross BOTH sides (rays) of the angle.
6. Without changing the size of the compass, place the compass point on the starting point (dot) on the reference line and swing an arc that will intersect the reference line and go above the reference line.
7. Go back to the given angle ∠ABC and measure the span (width) of the arc from where it crosses one side of the angle to where it crosses the other side of the angle. (Place a small arc to show you measured this distance.)
8. Using this width, place the compass point on the reference line where the previous arc crosses the reference line and mark off this new width on your new arc.
9. Connect this new intersection point to the starting point (dot) on your reference line.
10. Label your copy.

Proof of Construction: When your construction is finished, draw line segments connecting where the first arcs cross the sides of the angles. We know these lengths are the same in both drawings since they represent the measured spans of the same arcs. These addition of these segments will create two triangles that have 3 sets of congruent (equal) sides. Since the triangles are congruent by SSS and any leftover corresponding parts will also be congruent (by CPCTC), we know that ∠ABC is congruent to ∠A'B'C'.
(Note: These triangles are not necessarily ΔABC and ΔA'B'C', since the first arc in the construction need not pass through A and/or C on the given angle.)

{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-12-08T05:04:12+00:00","modifiedTime":"2016-12-08T05:04:12+00:00","timestamp":"2022-09-14T18:16:42+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"//dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"//dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Geometry","_links":{"self":"//dummies-api.dummies.com/v2/categories/33725"},"slug":"geometry","categoryId":33725}],"title":"How to Copy an Angle Using a Compass","strippedTitle":"how to copy an angle using a compass","slug":"copy-angle-using-compass","canonicalUrl":"","seo":{"metaDescription":"The basic idea behind copying a given angle is to use your compass to sort of measure how wide the angle is open; then you create another angle with the same am","noIndex":0,"noFollow":0},"content":"The basic idea behind copying a given angle is to use your compass to sort of measure how wide the angle is open; then you create another angle with the same amount of opening.\r\n\r\n<a href=\"//sg.cdnki.com/match-each-step-with-the-correct-ordered-description-for-how-to-construct-a-copy-of-an-angle---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzL0dFT00tM0VfMDA0Nl8wMS5naWY=.webp\"><img class=\"alignnone wp-image-230074 size-full\" src=\"//www.dummies.com/wp-content/uploads/GEOM-3E_0046_01.gif\" alt=\"geometry-angle-compass\" width=\"251\" height=\"45\" /></a>\r\n\r\nHere's the proof diagram.\r\n\r\n[caption id=\"attachment_229613\" align=\"aligncenter\" width=\"400\"]<a href=\"//sg.cdnki.com/match-each-step-with-the-correct-ordered-description-for-how-to-construct-a-copy-of-an-angle---aHR0cHM6Ly93d3cuZHVtbWllcy5jb20vd3AtY29udGVudC91cGxvYWRzLzk3ODExMTkxODE1NTItZmcyMDA4LmdpZg==.webp\"><img class=\"wp-image-229613 size-full\" src=\"//www.dummies.com/wp-content/uploads/9781119181552-fg2008.gif\" alt=\"geometry-copying-angle\" width=\"400\" height=\"536\" /></a> Copying an angle.[/caption]\r\n\r\nRefer to the figure as you work through these steps:\r\n<ol>\r\n\t<li><strong>Draw a working line, <em>l</em>, with point <em>B</em> on it.</strong></li>\r\n\t<li><strong>Open your compass to any radius <em>r,</em> and construct arc (<em>A</em>, <em>r</em>) intersecting the two sides of angle <em>A</em> at points <em>S</em> and <em>T.</em></strong></li>\r\n\t<li><strong>Construct arc (<em>B</em>, <em>r</em>) intersecting line <em>l</em> at some point <em>V.</em></strong></li>\r\n\t<li><strong>Construct arc (<em>S</em>, <em>ST</em>).</strong></li>\r\n\t<li><strong>Construct arc (<em>V</em>, <em>ST</em>) intersecting arc (<em>B</em>, <em>r</em>) at point <em>W.</em></strong></li>\r\n\t<li><strong>Draw line <em>BW</em> and you're done.</strong></li>\r\n</ol>","description":"The basic idea behind copying a given angle is to use your compass to sort of measure how wide the angle is open; then you create another angle with the same amount of opening.\r\n\r\n<a href=\"//www.dummies.com/wp-content/uploads/GEOM-3E_0046_01.gif\"><img class=\"alignnone wp-image-230074 size-full\" src=\"//www.dummies.com/wp-content/uploads/GEOM-3E_0046_01.gif\" alt=\"geometry-angle-compass\" width=\"251\" height=\"45\" /></a>\r\n\r\nHere's the proof diagram.\r\n\r\n[caption id=\"attachment_229613\" align=\"aligncenter\" width=\"400\"]<a href=\"//www.dummies.com/wp-content/uploads/9781119181552-fg2008.gif\"><img class=\"wp-image-229613 size-full\" src=\"//www.dummies.com/wp-content/uploads/9781119181552-fg2008.gif\" alt=\"geometry-copying-angle\" width=\"400\" height=\"536\" /></a> Copying an angle.[/caption]\r\n\r\nRefer to the figure as you work through these steps:\r\n<ol>\r\n\t<li><strong>Draw a working line, <em>l</em>, with point <em>B</em> on it.</strong></li>\r\n\t<li><strong>Open your compass to any radius <em>r,</em> and construct arc (<em>A</em>, <em>r</em>) intersecting the two sides of angle <em>A</em> at points <em>S</em> and <em>T.</em></strong></li>\r\n\t<li><strong>Construct arc (<em>B</em>, <em>r</em>) intersecting line <em>l</em> at some point <em>V.</em></strong></li>\r\n\t<li><strong>Construct arc (<em>S</em>, <em>ST</em>).</strong></li>\r\n\t<li><strong>Construct arc (<em>V</em>, <em>ST</em>) intersecting arc (<em>B</em>, <em>r</em>) at point <em>W.</em></strong></li>\r\n\t<li><strong>Draw line <em>BW</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&#45;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&#45;on&#45;one tutoring. He is a member of the Authors Guild and the National Council of Teachers of Mathematics. ","hasArticle":false,"_links":{"self":"//dummies-api.dummies.com/v2/authors/8957"}}],"primaryCategoryTaxonomy":{"categoryId":33725,"title":"Geometry","slug":"geometry","_links":{"self":"//dummies-api.dummies.com/v2/categories/33725"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":230072,"title":"How to Copy a Line Segment Using a Compass","slug":"copy-line-segment-using-compass","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/230072"}},{"articleId":230069,"title":"How to Find the Right Angle to Two Points","slug":"find-right-angle-two-points","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/230069"}},{"articleId":230066,"title":"Find the Locus of Points Equidistant from Two Points","slug":"find-locus-points-equidistant-two-points","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/230066"}},{"articleId":230063,"title":"How to Solve a Two-Dimensional Locus Problem","slug":"solve-two-dimensional-locus-problem","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/230063"}},{"articleId":230057,"title":"Find the Main Reflecting Line of a Glide Reflection","slug":"find-main-reflecting-line-glide-reflection","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/230057"}}],"fromCategory":[{"articleId":230072,"title":"How to Copy a Line Segment Using a Compass","slug":"copy-line-segment-using-compass","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/230072"}},{"articleId":230069,"title":"How to Find the Right Angle to Two Points","slug":"find-right-angle-two-points","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/230069"}},{"articleId":230066,"title":"Find the Locus of Points Equidistant from Two Points","slug":"find-locus-points-equidistant-two-points","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/230066"}},{"articleId":230063,"title":"How to Solve a Two-Dimensional Locus Problem","slug":"solve-two-dimensional-locus-problem","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/230063"}},{"articleId":230057,"title":"Find the Main Reflecting Line of a Glide Reflection","slug":"find-main-reflecting-line-glide-reflection","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"//dummies-api.dummies.com/v2/articles/230057"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":282230,"slug":"geometry-for-dummies-3rd-edition","isbn":"9781119181552","categoryList":["academics-the-arts","math","geometry"],"amazon":{"default":"//www.amazon.com/gp/product/1119181550/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"//www.amazon.ca/gp/product/1119181550/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"//www.tkqlhce.com/click-9208661-13710633?url=//www.chapters.indigo.ca/en-ca/books/product/1119181550-item.html&cjsku=978111945484","gb":"//www.amazon.co.uk/gp/product/1119181550/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"//www.amazon.de/gp/product/1119181550/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"//www.dummies.com/wp-content/uploads/geometry-for-dummies-3rd-edition-cover-9781119181552-201x255.jpg","width":201,"height":255},"title":"Geometry For Dummies","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"8957\">Mark Ryan </b>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 <i>Calculus For Dummies, Calculus Workbook For Dummies</i>, and <i>Geometry Workbook For Dummies</i>.</p>","authors":[{"authorId":8957,"name":"Mark Ryan","slug":"mark-ryan","description":" <p><b>Mark Ryan</b> has taught pre&#45;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&#45;on&#45;one tutoring. He is a member of the Authors Guild and the National Council of Teachers of Mathematics. ","hasArticle":false,"_links":{"self":"//dummies-api.dummies.com/v2/authors/8957"}}],"_links":{"self":"//dummies-api.dummies.com/v2/books/"}},"collections":[],"articleAds":{"footerAd":"<div class=\"du-ad-region row\" id=\"article_page_adhesion_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_adhesion_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;geometry&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119181552&quot;]}]\" id=\"du-slot-63221a8aad8e0\"></div></div>","rightAd":"<div class=\"du-ad-region row\" id=\"article_page_right_ad\"><div class=\"du-ad-unit col-md-12\" data-slot-id=\"article_page_right_ad\" data-refreshed=\"false\" \r\n data-target = \"[{&quot;key&quot;:&quot;cat&quot;,&quot;values&quot;:[&quot;academics-the-arts&quot;,&quot;math&quot;,&quot;geometry&quot;]},{&quot;key&quot;:&quot;isbn&quot;,&quot;values&quot;:[&quot;9781119181552&quot;]}]\" id=\"du-slot-63221a8ab0d5e\"></div></div>"},"articleType":{"articleType":"Articles","articleList":null,"content":null,"videoInfo":{"videoId":null,"name":null,"accountId":null,"playerId":null,"thumbnailUrl":null,"description":null,"uploadDate":null}},"sponsorship":{"sponsorshipPage":false,"backgroundImage":{"src":null,"width":0,"height":0},"brandingLine":"","brandingLink":"","brandingLogo":{"src":null,"width":0,"height":0},"sponsorAd":"","sponsorEbookTitle":"","sponsorEbookLink":"","sponsorEbookImage":{"src":null,"width":0,"height":0}},"primaryLearningPath":"Explore","lifeExpectancy":null,"lifeExpectancySetFrom":null,"dummiesForKids":"no","sponsoredContent":"no","adInfo":"","adPairKey":[]},"status":"publish","visibility":"public","articleId":230077},"articleLoadedStatus":"success"},"listState":{"list":{},"objectTitle":"","status":"initial","pageType":null,"objectId":null,"page":1,"sortField":"time","sortOrder":1,"categoriesIds":[],"articleTypes":[],"filterData":{},"filterDataLoadedStatus":"initial","pageSize":10},"adsState":{"pageScripts":{"headers":{"timestamp":"2022-11-21T10:50:01+00:00"},"adsId":0,"data":{"scripts":[{"pages":["all"],"location":"header","script":"<!--Optimizely Script-->\r\n<script src=\"//cdn.optimizely.com/js/10563184655.js\"></script>","enabled":false},{"pages":["all"],"location":"header","script":"<!-- comScore Tag -->\r\n<script>var _comscore = _comscore || [];_comscore.push({ c1: \"2\", c2: \"15097263\" });(function() {var s = document.createElement(\"script\"), el = document.getElementsByTagName(\"script\")[0]; s.async = true;s.src = (document.location.protocol == \"\" ? \"//sb\" : \"//b\") + \".scorecardresearch.com/beacon.js\";el.parentNode.insertBefore(s, el);})();</script><noscript><img src=\"//sb.scorecardresearch.com/p?c1=2&c2=15097263&cv=2.0&cj=1\" /></noscript>\r\n<!-- / comScore Tag -->","enabled":true},{"pages":["all"],"location":"footer","script":"<!--BEGIN QUALTRICS WEBSITE FEEDBACK SNIPPET-->\r\n<script type='text/javascript'>\r\n(function(){var g=function(e,h,f,g){\r\nthis.get=function(a){for(var a=a+\"=\",c=document.cookie.split(\";\"),b=0,e=c.length;b<e;b++){for(var d=c[b];\" \"==d.charAt(0);)d=d.substring(1,d.length);if(0==d.indexOf(a))return d.substring(a.length,d.length)}return null};\r\nthis.set=function(a,c){var b=\"\",b=new Date;b.setTime(b.getTime()+6048E5);b=\"; expires=\"+b.toGMTString();document.cookie=a+\"=\"+c+b+\"; path=/; \"};\r\nthis.check=function(){var a=this.get(f);if(a)a=a.split(\":\");else if(100!=e)\"v\"==h&&(e=Math.random()>=e/100?0:100),a=[h,e,0],this.set(f,a.join(\":\"));else return!0;var c=a[1];if(100==c)return!0;switch(a[0]){case \"v\":return!1;case \"r\":return c=a[2]%Math.floor(100/c),a[2]++,this.set(f,a.join(\":\")),!c}return!0};\r\nthis.go=function(){if(this.check()){var a=document.createElement(\"script\");a.type=\"text/javascript\";a.src=g;document.body&&document.body.appendChild(a)}};\r\nthis.start=function(){var t=this;\"complete\"!==document.readyState?window.addEventListener?window.addEventListener(\"load\",function(){t.go()},!1):window.attachEvent&&window.attachEvent(\"onload\",function(){t.go()}):t.go()};};\r\ntry{(new g(100,\"r\",\"QSI_S_ZN_5o5yqpvMVjgDOuN\",\"//zn5o5yqpvmvjgdoun-wiley.siteintercept.qualtrics.com/SIE/?Q_ZID=ZN_5o5yqpvMVjgDOuN\")).start()}catch(i){}})();\r\n</script><div id='ZN_5o5yqpvMVjgDOuN'><!--DO NOT REMOVE-CONTENTS PLACED HERE--></div>\r\n<!--END WEBSITE FEEDBACK SNIPPET-->","enabled":false},{"pages":["all"],"location":"header","script":"<!-- Hotjar Tracking Code for //www.dummies.com -->\r\n<script>\r\n (function(h,o,t,j,a,r){\r\n h.hj=h.hj||function(){(h.hj.q=h.hj.q||[]).push(arguments)};\r\n h._hjSettings={hjid:257151,hjsv:6};\r\n a=o.getElementsByTagName('head')[0];\r\n r=o.createElement('script');r.async=1;\r\n r.src=t+h._hjSettings.hjid+j+h._hjSettings.hjsv;\r\n a.appendChild(r);\r\n })(window,document,'//static.hotjar.com/c/hotjar-','.js?sv=');\r\n</script>","enabled":false},{"pages":["article"],"location":"header","script":"<!-- //Connect Container: dummies --> <script src=\"//get.s-onetag.com/bffe21a1-6bb8-4928-9449-7beadb468dae/tag.min.js\" async defer></script>","enabled":true},{"pages":["homepage"],"location":"header","script":"<meta name=\"facebook-domain-verification\" content=\"irk8y0irxf718trg3uwwuexg6xpva0\" />","enabled":true},{"pages":["homepage","article","category","search"],"location":"footer","script":"<!-- Facebook Pixel Code -->\r\n<noscript>\r\n<img height=\"1\" width=\"1\" src=\"//www.facebook.com/tr?id=256338321977984&ev=PageView&noscript=1\"/>\r\n</noscript>\r\n<!-- End Facebook Pixel Code -->","enabled":true}]}},"pageScriptsLoadedStatus":"success"},"navigationState":{"navigationCollections":[{"collectionId":287568,"title":"BYOB (Be Your Own Boss)","hasSubCategories":false,"url":"/collection/for-the-entry-level-entrepreneur-287568"},{"collectionId":293237,"title":"Be a Rad Dad","hasSubCategories":false,"url":"/collection/be-the-best-dad-293237"},{"collectionId":294090,"title":"Contemplating the Cosmos","hasSubCategories":false,"url":"/collection/theres-something-about-space-294090"},{"collectionId":287563,"title":"For Those Seeking Peace of Mind","hasSubCategories":false,"url":"/collection/for-those-seeking-peace-of-mind-287563"},{"collectionId":287570,"title":"For the Aspiring Aficionado","hasSubCategories":false,"url":"/collection/for-the-bougielicious-287570"},{"collectionId":291903,"title":"For the Budding Cannabis Enthusiast","hasSubCategories":false,"url":"/collection/for-the-budding-cannabis-enthusiast-291903"},{"collectionId":291934,"title":"For the Exam-Season Crammer","hasSubCategories":false,"url":"/collection/for-the-exam-season-crammer-291934"},{"collectionId":287569,"title":"For the Hopeless Romantic","hasSubCategories":false,"url":"/collection/for-the-hopeless-romantic-287569"},{"collectionId":287567,"title":"For the Unabashed Hippie","hasSubCategories":false,"url":"/collection/for-the-unabashed-hippie-287567"},{"collectionId":295430,"title":"Have a Beautiful (and Tasty) Thanksgiving","hasSubCategories":false,"url":"/collection/have-a-wonderful-thanksgiving-295430"}],"navigationCollectionsLoadedStatus":"success","navigationCategories":{"books":{"0":{"data":[{"categoryId":33512,"title":"Technology","hasSubCategories":true,"url":"/category/books/technology-33512"},{"categoryId":33662,"title":"Academics & The Arts","hasSubCategories":true,"url":"/category/books/academics-the-arts-33662"},{"categoryId":33809,"title":"Home, Auto, & Hobbies","hasSubCategories":true,"url":"/category/books/home-auto-hobbies-33809"},{"categoryId":34038,"title":"Body, Mind, & Spirit","hasSubCategories":true,"url":"/category/books/body-mind-spirit-34038"},{"categoryId":34224,"title":"Business, Careers, & Money","hasSubCategories":true,"url":"/category/books/business-careers-money-34224"}],"breadcrumbs":[],"categoryTitle":"Level 0 Category","mainCategoryUrl":"/category/books/level-0-category-0"}},"articles":{"0":{"data":[{"categoryId":33512,"title":"Technology","hasSubCategories":true,"url":"/category/articles/technology-33512"},{"categoryId":33662,"title":"Academics & The Arts","hasSubCategories":true,"url":"/category/articles/academics-the-arts-33662"},{"categoryId":33809,"title":"Home, Auto, & Hobbies","hasSubCategories":true,"url":"/category/articles/home-auto-hobbies-33809"},{"categoryId":34038,"title":"Body, Mind, & Spirit","hasSubCategories":true,"url":"/category/articles/body-mind-spirit-34038"},{"categoryId":34224,"title":"Business, Careers, & Money","hasSubCategories":true,"url":"/category/articles/business-careers-money-34224"}],"breadcrumbs":[],"categoryTitle":"Level 0 Category","mainCategoryUrl":"/category/articles/level-0-category-0"}}},"navigationCategoriesLoadedStatus":"success"},"searchState":{"searchList":[],"searchStatus":"initial","relatedArticlesList":[],"relatedArticlesStatus":"initial"},"routeState":{"name":"Article3","path":"/article/academics-the-arts/math/geometry/copy-angle-using-compass-230077/","hash":"","query":{},"params":{"category1":"academics-the-arts","category2":"math","category3":"geometry","article":"copy-angle-using-compass-230077"},"fullPath":"/article/academics-the-arts/math/geometry/copy-angle-using-compass-230077/","meta":{"routeType":"article","breadcrumbInfo":{"suffix":"Articles","baseRoute":"/category/articles"},"prerenderWithAsyncData":true},"from":{"name":null,"path":"/","hash":"","query":{},"params":{},"fullPath":"/","meta":{}}},"dropsState":{"submitEmailResponse":false,"status":"initial"},"sfmcState":{"status":"initial"},"profileState":{"auth":{},"userOptions":{},"status":"success"}}