[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-538006-105":59,"doc-detail-538006-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","samples-to-success-geometry-mathematics-high-school-geometry","Samples to Success - GEOMETRY - Mathematics High School - Geometry","","Samples to Success provides sample classroom and assessment items designed to show how students engage with different texts, tasks, and learning contexts. The geometry section presents question types aligned with ACT-style expectations and highlights the math proficiency students must demonstrate. Items emphasize defining and applying shape and solid concepts, using relationships such as congruence and similarity, calculating surface area and volume, and solving problems involving triangles, circles, conic sections, and coordinate geometry. It includes instructional guidance and sample multiple-choice questions.",{"@graph":69,"@context":122},[70,84,105],{"@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/samples-to-success-geometry-mathematics-high-school-geometry/538006/",{"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/samples-to-success-geometry-mathematics-high-school-geometry/538006.png","ImageObject",300,407,{"name":92,"@type":93},"hdkawk","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-10",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What kinds of skills do the geometry sample questions focus on?","Question",{"text":112,"@type":113},"They focus on defining and applying knowledge of shapes and solids, including congruence and similarity, and measuring surface area and volume.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are coordinate plane problems used in the geometry section?",{"text":117,"@type":113},"Students work with points, translations, midpoints, ellipses, and related geometric features on the standard coordinate plane.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the source and purpose of these sample items?",{"text":121,"@type":113},"The document includes ACT-style items intended for classroom instruction and references ACT alignment guides to support understanding of proficiency expectations.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},538006,1791819663,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":39,"preview_page_count":4},3985747859855,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Samples to Success  \nSample items provide valuable insight into how students engage with different texts, tasks, and contexts by highlighting the types of opportunities they need for success in the classroom. These items offer a shared reference point for understanding proficiency expectations, complementing the assessment's role in measuring learning. Analyzing items alongside performance data can enable educators to gain a deeper understanding of students' strengths and areas for growth. Students thrive in environments rich with diverse materials, challenges that vary in task type, and multiple avenues for demonstrating understanding. High-quality instruction, aligned with the learning goals, is the most effective way to support students' growth and prepare them for success.  \nGEOMETRY  \nThe sample questions included in this rubric are a blend of those typical of the ACT and others that are suitable for classroom instruction, aimed at reinforcing and developing the skills assessed on the ACT. The geometry content includes asking students to define and apply knowledge of shapes and solids, such as congruence and similarity relationships or surface area and volume measurements. Students must understand the composition of objects, and solve for missing values in triangles, circles, and other figures, including using trigonometric ratios and equations of conic sections. This document contains ACT items and includes excerpts from ACT alignment guides: © ACT Education Corp.  \nMATHEMATICS HIGH SCHOOL  \nGeometry  \nBelow Proficient Approaching Proficient Proficient Above Proficient  \nIn the standard (􀝔, 􀝕) coordinate plane, point A has coordinates (-7, -5) . Point Ais translated 7 units to the left and 5 units down, and the image is labeled 􀜣 ’. What are the coordinates of 􀜣 ’?  \nA. (-14, -10)  \nB. (-12, -12)  \nC. (-7, -10)  \nD. (0,0)  \nE. (14,10)  \nIn the standard (􀝔, 􀝕) coordinate plane, what is the midpoint of the line segment that has endpoints (3,8) and (1, -4)?  \nA. (-2, -12)  \nB. (-1, -6)  \nC. (121 , − 32)  \nD. (2,2)  \nE. (4, -12)  \nIn the standard (x,y) coordinate plane, the point (2,1) is the midpoint of ̅̅􀜥̅̅􀜦 . Point C has coordinates (6,8) . What are the coordinates of point D?  \nA. (-2, − 72)  \nB. (-2, -6)  \nC. (4, 92)  \nD. (10,10)  \nE. (10,15)  \nThe ellipse in the standard (􀝔, 􀝕) coordinate plane below is the graph of (􀯫−255)2 + (􀯬3)2 = 1. Which of the following points are the foci of the ellipse?  \nA. (0,3) and (5 .3)  \nB. (0,3) and (10,3)  \nC. (1,3) and (5,0)  \nD. (1,3) and (9,3)  \nE. (5,0) and (5,6)  \nGeometry  \nBelow Proficient Approaching Proficient Proficient Above Proficient  \nIf o = 10 􀝂􀝐 and a = 17 􀝂􀝐, how long is side ℎ?  \nA. 17.9 ft  \nB. Not enough information to solve.  \nC. 19.3 ft  \nD. 19.7 ft  \nE. 18 ft  \nThe radius of the base of the right circular cone shown below is 5 inches, and the height of the cone is 7 inches. Solving which of the following equations gives the measure, 􀟠 , of the angle formed by a slant height of the cone anda radius?  \nA. tan Ɵ = 57 B. tan Ɵ =   \n7 5  \nC. sin Ɵ =  \nD. sin Ɵ =  \nE. cos Ɵ =  \n5 7  \n7 5  \n7 5  \nA 12-foot taut wire has one end attached to the ground and the other end attached to a vertical pole, as shown below. The point of contact of the wire and the pole is 9 feet above the ground. What angle does the wire make with the level ground?  \nIn ∆􀜲􀜳􀜴 shown below, the measure of ∠ 􀜲 is 40° . PR = 110 meters, and the measure of ∠ 􀜴 is 80° . Which of the following expressions gives QR, in meters?  \n(Note: For triangle with sides of length 􀜽,􀜾 , and 􀜿 that are opposite angles ∠􀜣 ,∠􀜤 , ∠C, respectively, sin􀯔∠􀮺 = sin􀯕∠􀮻 = sin􀯖∠􀮼~~ ~~ .)  \n110 sin 40° A. ~~ ~~  \nsin 60°  \n110 sin 40° B. ~~ ~~  \nsin 80°  \n110 sin 60° C. ~~ ~~  \nsin 40°  \n110 sin 80° D. ~~ ~~  \nsin 40°  \n110 sin 80° E. ~~ ~~  \nsin 60°  \nGeometry  \nBelow Proficient Approaching Proficient Proficient Above Proficient  \nThe perimeter of a regular pentagon is  \n85. What is the length of one side?  \nA. 8.5  \nB. 15√3  \nC.","cbCaiipR0x5ZyS7Y","https://ap.wps.com/l/cbCaiipR0x5ZyS7Y","pdf",332006,"English","# Geometry\n## Mathematics High School\n## Sample Questions (Multiple Choice)","[{\"question\":\"What kinds of skills do the geometry sample questions focus on?\",\"answer\":\"They focus on defining and applying knowledge of shapes and solids, including congruence and similarity, and measuring surface area and volume.\"},{\"question\":\"How are coordinate plane problems used in the geometry section?\",\"answer\":\"Students work with points, translations, midpoints, ellipses, and related geometric features on the standard coordinate plane.\"},{\"question\":\"What is the source and purpose of these sample items?\",\"answer\":\"The document includes ACT-style items intended for classroom instruction and references ACT alignment guides to support understanding of proficiency expectations.\"}]","Samples to Success - GEOMETRY - Mathematics High School - Geometry | PDF",1791605977]