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C. Escher and patterns from Islamic art. The lesson explains triangle parts—vertices, sides, and angles—and how to name triangles, classify them by angles and sides, and recognize special isosceles triangle terminology. Practice activities and exercises reinforce angle measures and multi-step equation solving.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/lesson-5-1-classifying-triangles/386804/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/lesson-5-1-classifying-triangles/386804.png","ImageObject",300,407,{"name":92,"@type":93},"Aurelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-24",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How are triangles classified by their angles?","Question",{"text":113,"@type":114},"Triangles are classified as acute, obtuse, or right based on how many angles are acute and which angle type is present as the third angle.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What special parts are identified in an isosceles triangle?",{"text":118,"@type":114},"The angle formed by the congruent sides is the vertex angle, the congruent sides are the legs, the two angles at the base are base angles, and the side opposite the vertex angle is the base.",{"name":120,"@type":111,"acceptedAnswer":121},"How can you find the measures of sides of an isosceles triangle using equations?",{"text":122,"@type":114},"Use the fact that the sides determined by the expressions are congruent (for example, AB equals BC). Set up an equation involving the expressions, solve for the variable, and substitute back to compute the side measures.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},386804,1790639270,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":36,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},1099514068365,"https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?_k=1776742907772140068","C H A P T E R  \nMake this Foldable to help you organize information about the material in this chapter. Begin with a sheet of plain 8 \" by 11\" paper.  \n➊  \n➋  \n➌  \n➍  \nFold in half lengthwise.  \nFold the top to the bottom.  \nOpen and cut along the second fold to make two tabs.  \nLabel each tab as shown.  \nReading and Writing As you read and study the chapter, write what you learn about the two methods of classifying triangles.  \n186 Chapter 5 Triangles and Congruence  \nProblem-Solving Workshop  \nProject  \nYour school is sponsoring a Geometry and the Arts week and is awarding a prize for the best design. The only guideline is that the design must be composed of triangles. Make a design that is composed of triangles.  \nWorking on the Project  \nWork with a partner and develop a plan. Here are some suggestions to help you get started.  \n• Research the works of Dutch artist  \nM. C. Escher.  \n• Research how repeating patterns of triangles are used in Islamic art and architecture. You may also want to do research about geometric patterns that are common to your ethnic heritage.  \nTechnology Tools  \n• Use an electronic encyclopedia to do your research.  \n• Use The Geometer’s Sketchpad or other drawing software to complete your design.  \nResearch For more information about M. C. Escher, visit:  \n[www.geomconcepts.com](www.geomconcepts.com)  \nPresenting the Project    \nDraw your design on unlined paper. Write a paragraph that contains the following information about your design:  \n• classification of the triangles by their angles and sides,• an explanation of how slides, flips, or turns are used, and • some examples of congruent triangles.  \nChapter 5 Problem-Solving Workshop 187  \n5 1 Classifying Triangles  \nWhat You’ll Learn  \nYou’ll learn to identify the parts of trianglesand to classify triangles by their parts.  \nWhy It’s Important  \nArt Abstract artists use geometric shapes in their designs. See Exercise 24.  \nRead the symbol 􀀁 as triangle. Other names for  \n􀀁DEF are 􀀁FDE, 􀀁EDF,􀀁FED, 􀀁DFE, and  \n􀀁EFD.  \nOptical art is a form of abstract art that creates special effects by using geometric patterns. The design at the right looks like a spiral staircase, but it is made mostly of triangles.  \nIn geometry, a triangle is a figure formed when three noncollinear points are connected by segments. Each pair of segments forms an angle of the triangle. The vertex of each angle is a vertex of the triangle.  \nTriangles are named by the letters at their vertices. Triangle DEF, written 􀀁DEF, is shown below.  \nvertexE  \nside  \nD F  \nThe sides are DE, EF, and DF. The vertices are D, E, and F. The angles are 􀀂D, 􀀂E, and 􀀂F.  \nIn Chapter 3, you classified angles as acute, obtuse, or right. Triangles can also be classified by their angles. All triangles have at least two acute angles. The third angle is either acute, obtuse, or right.  \nTriangles Classified by Angles  \nacute  \nall acute angles  \nobtuse  \none obtuse angle  \nright  \none right angle  \n188 Chapter 5 Triangles and Congruence  \nSince all sides of an equilateral triangle are congruent, then at least two of its sides are congruent. So, all equilateral triangles are also isosceles triangles.  \nSome parts of isosceles triangles have special names.  \nThe angle formed by the congruent sides is called the vertex angle.  \nThe congruent sides  \nare called legs. leg  leg  \nThe two angles formed by the base and one of the congruent sides are called base angles.  \nbase angle    base angle  \nThe side opposite the vertex  \nangle is called the base.  \nClassify each triangle by its angles and by its sides.  \nE  \nF  \nG  \n􀀁EFG is a right isosceles triangle.  \n2 C  \nA B  \n􀀁ABC is an acute equilateral triangle.  \na. X  \n25˚  \nZ Y  \nb.  \nL  \nM  \nN  \n50 ˚ 40 ˚  \n60 ˚  \n60 ˚ 60 ˚  \nExamples  \n1  \n[www.geomconcepts.com/extra_examples](www.geomconcepts.com/extra_examples)  \nLesson 5–1 Classifying Triangles 189  \nFind the measures of  and  of isosceles triangle ABC if 􀀁A is the vertex angle.  \nExplore You know that ","cbCaiqAu6RWDyopp","https://ap.wps.com/l/cbCaiqAu6RWDyopp","pdf",7255445,"English","# Problem-Solving Workshop\n## Project and research tasks\n## Presenting the project\n# 5.1 Classifying Triangles\n## What you’ll learn and why it’s important\n## Triangle definition and naming\n## Classification by angles\n## Isosceles triangle parts\n## Examples and guided practice\n## Check for understanding\n## Exercises and applications","[{\"question\":\"How are triangles classified by their angles?\",\"answer\":\"Triangles are classified as acute, obtuse, or right based on how many angles are acute and which angle type is present as the third angle.\"},{\"question\":\"What special parts are identified in an isosceles triangle?\",\"answer\":\"The angle formed by the congruent sides is the vertex angle, the congruent sides are the legs, the two angles at the base are base angles, and the side opposite the vertex angle is the base.\"},{\"question\":\"How can you find the measures of sides of an isosceles triangle using equations?\",\"answer\":\"Use the fact that the sides determined by the expressions are congruent (for example, AB equals BC). Set up an equation involving the expressions, solve for the variable, and substitute back to compute the side measures.\"}]","Lesson 5-1 - Classifying Triangles | PDF",1790276260,101]