{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T07:10:36+00:00","modifiedTime":"2016-03-26T07:10:36+00:00","timestamp":"2022-09-14T17:46:05+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 with Proportional Triangles — Practice Geometry Questions","strippedTitle":"proofs with proportional triangles — practice geometry questions","slug":"proofs-with-proportional-triangles-practice-geometry-questions","canonicalUrl":"","seo":{"metaDescription":"Say that you have two triangles and you need to prove that the sides of the triangles are in proportion to each other. How do you do it? Elementary! You just ne","noIndex":0,"noFollow":0},"content":"<p>Say that you have two triangles and you need to prove that the sides of the triangles are in proportion to each other. How do you do it? Elementary! You just need to prove the triangles are similar by AA (angle-angle).</p>\n<p class=\"Remember\">If two triangles are similar, this means the corresponding sides are in proportion.</p>\n<p>The following practice problem asks you to finish a proof showing the sides of two triangles are in proportion.</p>\n<h2 id=\"tab1\" >Practice questions</h2>\n<p>Complete the following proof by giving the missing statements and reasons.</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501386.image0.png\" height=\"222\" alt=\"image0.png\" width=\"250\"/>\n<p>Given:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501387.image1.png\" height=\"96\" alt=\"image1.png\" width=\"144\"/>\n<p>Fill in the blanks in the table by answering the following questions. </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501388.image2.png\" height=\"307\" alt=\"image2.png\" width=\"424\"/>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">What is the missing angle in Statement 2?</p>\n </li>\n <li><p class=\"first-para\">What is the statement for Reason 3?</p>\n </li>\n <li><p class=\"first-para\">What is the reason for Statement 4?</p>\n </li>\n <li><p class=\"first-para\">What is the reason for Statement 6?</p>\n </li>\n <li><p class=\"first-para\">What is the reason for Statement 7?</p>\n </li>\n</ol>\n<h2 id=\"tab2\" >Answers and explanations</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\"></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501389.image3.png\" height=\"17\" alt=\"image3.png\" width=\"49\"/>\n<p class=\"child-para\">When two lines intersect, they form vertical angles across from each other.</p>\n </li>\n <li><p class=\"first-para\"></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501390.image4.png\" height=\"19\" alt=\"image4.png\" width=\"103\"/>\n<p class=\"child-para\">You know that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501391.image5.png\" height=\"19\" alt=\"image5.png\" width=\"117\"/>\n<p class=\"child-para\">are vertical angles. </p>\n<p class=\"child-para\">You also know that if two angles are vertical angles, they're congruent, so </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501392.image6.png\" height=\"19\" alt=\"image6.png\" width=\"100\"/>\n </li>\n <li><p class=\"first-para\">Perpendicular lines form right angles.</p>\n<p class=\"child-para\">When two perpendicular lines intersect, they create right angles.</p>\n </li>\n <li><p class=\"first-para\">AA</p>\n<p class=\"child-para\">If two angles of a triangle are congruent to two angles of a different triangle, the two triangles are similar.</p>\n </li>\n <li><p class=\"first-para\">If two triangles are similar, their sides are in proportion.</p>\n </li>\n</ol>","description":"<p>Say that you have two triangles and you need to prove that the sides of the triangles are in proportion to each other. How do you do it? Elementary! You just need to prove the triangles are similar by AA (angle-angle).</p>\n<p class=\"Remember\">If two triangles are similar, this means the corresponding sides are in proportion.</p>\n<p>The following practice problem asks you to finish a proof showing the sides of two triangles are in proportion.</p>\n<h2 id=\"tab1\" >Practice questions</h2>\n<p>Complete the following proof by giving the missing statements and reasons.</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501386.image0.png\" height=\"222\" alt=\"image0.png\" width=\"250\"/>\n<p>Given:</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501387.image1.png\" height=\"96\" alt=\"image1.png\" width=\"144\"/>\n<p>Fill in the blanks in the table by answering the following questions. </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501388.image2.png\" height=\"307\" alt=\"image2.png\" width=\"424\"/>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">What is the missing angle in Statement 2?</p>\n </li>\n <li><p class=\"first-para\">What is the statement for Reason 3?</p>\n </li>\n <li><p class=\"first-para\">What is the reason for Statement 4?</p>\n </li>\n <li><p class=\"first-para\">What is the reason for Statement 6?</p>\n </li>\n <li><p class=\"first-para\">What is the reason for Statement 7?</p>\n </li>\n</ol>\n<h2 id=\"tab2\" >Answers and explanations</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\"></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501389.image3.png\" height=\"17\" alt=\"image3.png\" width=\"49\"/>\n<p class=\"child-para\">When two lines intersect, they form vertical angles across from each other.</p>\n </li>\n <li><p class=\"first-para\"></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501390.image4.png\" height=\"19\" alt=\"image4.png\" width=\"103\"/>\n<p class=\"child-para\">You know that </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501391.image5.png\" height=\"19\" alt=\"image5.png\" width=\"117\"/>\n<p class=\"child-para\">are vertical angles. </p>\n<p class=\"child-para\">You also know that if two angles are vertical angles, they're congruent, so </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501392.image6.png\" height=\"19\" alt=\"image6.png\" width=\"100\"/>\n </li>\n <li><p class=\"first-para\">Perpendicular lines form right angles.</p>\n<p class=\"child-para\">When two perpendicular lines intersect, they create right angles.</p>\n </li>\n <li><p class=\"first-para\">AA</p>\n<p class=\"child-para\">If two angles of a triangle are congruent to two angles of a different triangle, the two triangles are similar.</p>\n </li>\n <li><p class=\"first-para\">If two triangles are similar, their sides are in proportion.</p>\n </li>\n</ol>","blurb":"","authors":[{"authorId":8986,"name":"Allen Ma","slug":"allen-ma","description":" <p><b>Allen Ma </b>and<b> Amber Kuang </b>are math teachers at John F. Kennedy High School in Bellmore, NY. Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8986"}},{"authorId":8987,"name":"Amber Kuang","slug":"amber-kuang","description":" <p><b>Allen Ma </b>and<b> Amber Kuang </b>are math teachers at John F. Kennedy High School in Bellmore, NY. Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years.</p> ","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-9781118853269-193x255.jpg","width":193,"height":255},"title":"Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"8986\">Allen Ma</b> and <b data-author-id=\"8987\">Amber Kuang</b> are math teachers at John F. 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Proofs with Proportional Triangles — Practice Geometry Questions

By: Allen Ma and Amber Kuang and

Updated: 03-26-2016

From The Book: Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)

Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)

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Say that you have two triangles and you need to prove that the sides of the triangles are in proportion to each other. How do you do it? Elementary! You just need to prove the triangles are similar by AA (angle-angle).

If two triangles are similar, this means the corresponding sides are in proportion.

The following practice problem asks you to finish a proof showing the sides of two triangles are in proportion.

Practice questions

Complete the following proof by giving the missing statements and reasons.

Given:

Fill in the blanks in the table by answering the following questions.

What is the missing angle in Statement 2?
What is the statement for Reason 3?
What is the reason for Statement 4?
What is the reason for Statement 6?
What is the reason for Statement 7?

Answers and explanations

When two lines intersect, they form vertical angles across from each other.
You know that

are vertical angles.

You also know that if two angles are vertical angles, they're congruent, so
Perpendicular lines form right angles.

When two perpendicular lines intersect, they create right angles.
AA

If two angles of a triangle are congruent to two angles of a different triangle, the two triangles are similar.
If two triangles are similar, their sides are in proportion.

About This Article

This article is from the book:

Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice) ,

About the book authors:

Allen Ma and Amber Kuang are math teachers at John F. Kennedy High School in Bellmore, New York. Allen, who has taught geometry for 20 years, is the math team coach and a former honors math research coordinator. Amber has taught all levels of mathematics, from algebra to calculus, for the past 14 years.

This article can be found in the category:

Geometry ,