Proofs Involving the Triangle Inequality Theorem — Practice Geometry Questions

{“appState”:{“pageLoadApiCallsStatus”:true},”articleState”:{“article”:{“headers”:{“creationTime”:”2016-03-26T07:10:06+00:00″,”modifiedTime”:”2016-03-26T07:10:06+00:00″,”timestamp”:”2022-09-14T17:46:02+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”:”Proofs Involving the Triangle Inequality Theorem — Practice Geometry Questions”,”strippedTitle”:”proofs involving the triangle inequality theorem — practice geometry questions”,”slug”:”proofs-involving-the-triangle-inequality-theorem-practice-geometry-questions”,”canonicalUrl”:””,”seo”:{“metaDescription”:”In geometry, the triangle inequality theorem states that when you add the lengths of any two sides of a triangle, their sum will be greater that the length of t”,”noIndex”:0,”noFollow”:0},”content”:”In geometry, the triangle inequality theorem states that when you add the lengths of any two sides of a triangle, their sum will be greater that the length of the third side.\nBy using the triangle inequality theorem and the exterior angle theorem, you should have no trouble completing the inequality proof in the following practice question.\n<h2 id=\”tab1\” >Practice questions</h2>\nComplete the following proof by adding the missing statement or reason.\n<img src=\”https://www.dummies.com/wp-content/uploads/501462.image0.png\” height=\”246\” alt=\”image0.png\” width=\”250\”/>\nGiven: \n<img src=\”https://www.dummies.com/wp-content/uploads/501463.image1.png\” height=\”24\” alt=\”image1.png\” width=\”165\”/>\nProve: ET > TV\n<img src=\”https://www.dummies.com/wp-content/uploads/501464.image2.png\” height=\”241\” alt=\”image2.png\” width=\”360\”/>\n<ol class=\”level-one\”>\n <li>What is the statement for Reason 2?\n </li>\n <li>What is the reason for Statement 3?\n </li>\n <li>What is the missing angle in Statement 4?\n </li>\n <li>What is the reason for Statement 5?\n </li>\n <li>What is the reason for Statement 6?\n </li>\n</ol>\n<h2 id=\”tab2\” >Answers and explanations</h2>\n<ol class=\”level-one\”>\n <li>\n<img src=\”https://www.dummies.com/wp-content/uploads/501465.image3.png\” height=\”17\” alt=\”image3.png\” width=\”63\”/>\nA bisector divides an angle into two congruent angles.\n </li>\n <li>The exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles.\n<img src=\”https://www.dummies.com/wp-content/uploads/501466.image4.png\” height=\”21\” alt=\”image4.png\” width=\”285\”/>\nare the two nonadjacent interior angles of \n<img src=\”https://www.dummies.com/wp-content/uploads/501467.image5.png\” height=\”19\” alt=\”image5.png\” width=\”44\”/>\nThe exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles of the triangle; therefore, \n<img src=\”https://www.dummies.com/wp-content/uploads/501468.image6.png\” height=\”16\” alt=\”image6.png\” width=\”127\”/>\n </li>\n <li>\n<img src=\”https://www.dummies.com/wp-content/uploads/501469.image7.png\” height=\”17\” alt=\”image7.png\” width=\”27\”/>\nYou found that \n<img src=\”https://www.dummies.com/wp-content/uploads/501470.image8.png\” height=\”16\” alt=\”image8.png\” width=\”127\”/>\nThe whole is greater than its parts, which means that\n<img src=\”https://www.dummies.com/wp-content/uploads/501471.image9.png\” height=\”16\” alt=\”image9.png\” width=\”85\”/>\n </li>\n <li>Transitive property\nBecause \n<img src=\”https://www.dummies.com/wp-content/uploads/501472.image10.png\” height=\”19\” alt=\”image10.png\” width=\”172\”/>\nthe transitive property finds that \n<img src=\”https://www.dummies.com/wp-content/uploads/501473.image11.png\” height=\”16\” alt=\”image11.png\” width=\”85\”/>\n </li>\n <li>In a triangle, the longest side is opposite the largest angle.\n<img src=\”https://www.dummies.com/wp-content/uploads/501474.image12.png\” height=\”25\” alt=\”image12.png\” width=\”276\”/>\nYou discovered that \n<img src=\”https://www.dummies.com/wp-content/uploads/501475.image13.png\” height=\”16\” alt=\”image13.png\” width=\”85\”/>\nIn a triangle, the longest side is opposite the largest angle, so ET > TV.\n </li>\n</ol>”,”description”:”In geometry, the triangle inequality theorem states that when you add the lengths of any two sides of a triangle, their sum will be greater that the length of the third side.\nBy using the triangle inequality theorem and the exterior angle theorem, you should have no trouble completing the inequality proof in the following practice question.\n<h2 id=\”tab1\” >Practice questions</h2>\nComplete the following proof by adding the missing statement or reason.\n<img src=\”https://www.dummies.com/wp-content/uploads/501462.image0.png\” height=\”246\” alt=\”image0.png\” width=\”250\”/>\nGiven: \n<img src=\”https://www.dummies.com/wp-content/uploads/501463.image1.png\” height=\”24\” alt=\”image1.png\” width=\”165\”/>\nProve: ET > TV\n<img src=\”https://www.dummies.com/wp-content/uploads/501464.image2.png\” height=\”241\” alt=\”image2.png\” width=\”360\”/>\n<ol class=\”level-one\”>\n <li>What is the statement for Reason 2?\n </li>\n <li>What is the reason for Statement 3?\n </li>\n <li>What is the missing angle in Statement 4?\n </li>\n <li>What is the reason for Statement 5?\n </li>\n <li>What is the reason for Statement 6?\n </li>\n</ol>\n<h2 id=\”tab2\” >Answers and explanations</h2>\n<ol class=\”level-one\”>\n <li>\n<img src=\”https://www.dummies.com/wp-content/uploads/501465.image3.png\” height=\”17\” alt=\”image3.png\” width=\”63\”/>\nA bisector divides an angle into two congruent angles.\n </li>\n <li>The exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles.\n<img src=\”https://www.dummies.com/wp-content/uploads/501466.image4.png\” height=\”21\” alt=\”image4.png\” width=\”285\”/>\nare the two nonadjacent interior angles of \n<img src=\”https://www.dummies.com/wp-content/uploads/501467.image5.png\” height=\”19\” alt=\”image5.png\” width=\”44\”/>\nThe exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles of the triangle; therefore, \n<img src=\”https://www.dummies.com/wp-content/uploads/501468.image6.png\” height=\”16\” alt=\”image6.png\” width=\”127\”/>\n </li>\n <li>\n<img src=\”https://www.dummies.com/wp-content/uploads/501469.image7.png\” height=\”17\” alt=\”image7.png\” width=\”27\”/>\nYou found that \n<img src=\”https://www.dummies.com/wp-content/uploads/501470.image8.png\” height=\”16\” alt=\”image8.png\” width=\”127\”/>\nThe whole is greater than its parts, which means that\n<img src=\”https://www.dummies.com/wp-content/uploads/501471.image9.png\” height=\”16\” alt=\”image9.png\” width=\”85\”/>\n </li>\n <li>Transitive property\nBecause \n<img src=\”https://www.dummies.com/wp-content/uploads/501472.image10.png\” height=\”19\” alt=\”image10.png\” width=\”172\”/>\nthe transitive property finds that \n<img src=\”https://www.dummies.com/wp-content/uploads/501473.image11.png\” height=\”16\” alt=\”image11.png\” width=\”85\”/>\n </li>\n <li>In a triangle, the longest side is opposite the largest angle.\n<img src=\”https://www.dummies.com/wp-content/uploads/501474.image12.png\” height=\”25\” alt=\”image12.png\” width=\”276\”/>\nYou discovered that \n<img src=\”https://www.dummies.com/wp-content/uploads/501475.image13.png\” height=\”16\” alt=\”image13.png\” width=\”85\”/>\nIn a triangle, the longest side is opposite the largest angle, so ET > TV.\n </li>\n</ol>”,”blurb”:””,”authors”:[{“authorId”:8986,”name”:”Allen Ma”,”slug”:”allen-ma”,”description”:” Allen Ma and Amber Kuang are math teachers at John F. 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Amber has taught all levels of math, from algebra to calculus, for 20 years. “,”hasArticle”:false,”_links”:{“self”:”https://dummies-api.dummies.com/v2/authors/8987″}}],”primaryCategoryTaxonomy”:{“categoryId”:33725,”title”:”Geometry”,”slug”:”geometry”,”_links”:{“self”:”https://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”:[{“label”:”Practice questions”,”target”:”#tab1″},{“label”:”Answers and explanations”,”target”:”#tab2″}],”relatedArticles”:{“fromBook”:[{“articleId”:207513,”title”:”Geometry: 1001 Practice Problems For Dummies Cheat Sheet”,”slug”:”1001-geometry-practice-problems-for-dummies-cheat-sheet”,”categoryList”:[“academics-the-arts”,”math”,”geometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/207513″}},{“articleId”:144555,”title”:”Circle Basics for Geometry Problems”,”slug”:”circle-basics-for-geometry-problems”,”categoryList”:[“academics-the-arts”,”math”,”geometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/144555″}},{“articleId”:144556,”title”:”Coordinate Geometry Formulas”,”slug”:”coordinate-geometry-formulas”,”categoryList”:[“academics-the-arts”,”math”,”geometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/144556″}},{“articleId”:144557,”title”:”Geometry Practice Problems with Triangles and Polygons”,”slug”:”geometry-practice-problems-with-triangles-and-polygons”,”categoryList”:[“academics-the-arts”,”math”,”geometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/144557″}},{“articleId”:143448,”title”:”Formulas for Geometric Solids Problems”,”slug”:”formulas-for-geometric-solids-problems”,”categoryList”:[“academics-the-arts”,”math”,”geometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/143448″}}],”fromCategory”:[{“articleId”:230077,”title”:”How to Copy an Angle Using a Compass”,”slug”:”copy-angle-using-compass”,”categoryList”:[“academics-the-arts”,”math”,”geometry”],”_links”:{“self”:”https://dummies-api.dummies.com/v2/articles/230077″}},{“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”:”https://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”:”https://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”:”https://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”:”https://dummies-api.dummies.com/v2/articles/230063″}}]},”hasRelatedBookFromSearch”:false,”relatedBook”:{“bookId”:281917,”slug”:”geometry-1001-practice-problems-for-dummies-free-online-practice”,”isbn”:”9781118853269″,”categoryList”:[“academics-the-arts”,”math”,”geometry”],”amazon”:{“default”:”https://www.amazon.com/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20″,”ca”:”https://www.amazon.ca/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20″,”indigo_ca”:”http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1118853261-item.html&cjsku=978111945484″,”gb”:”https://www.amazon.co.uk/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20″,”de”:”https://www.amazon.de/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20″},”image”:{“src”:”https://www.dummies.com/wp-content/uploads/geometry-1001-practice-problems-for-dummies-cover-9781118853269-193×255.jpg”,”width”:193,”height”:255},”title”:”Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)”,”testBankPinActivationLink”:””,”bookOutOfPrint”:false,”authorsInfo”:”Allen Ma and Amber Kuang are math teachers at John F. 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Proofs Involving the Triangle Inequality Theorem — Practice Geometry Questions

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