[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207783-en":3,"doc-seo-207783-105":30,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207783,962085571259,"Putri","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",4,"Exam","Circle Theorems: The Alternate Segment Theorem","This document focuses on the theorem of alternate segments in circles. It is designed for Year 10 students as part of their Key Stage 4 mathematics curriculum. The material is presented by Mr. Chan and aims to deepen students' understanding of circle theorems. It includes exercises that require students to shade specific angles formed by chords and tangents, and angles subtended by chords at the circumference. Additionally, students are tasked with calculating the size of marked angles, providing justifications for their answers based on geometric principles, and proving the alternate segment theorem itself. The document emphasizes the relationship between the alternate segment theorem and the property that angles in a triangle sum to 180 degrees. The exercises are structured to progressively build knowledge and skills, moving from visual identification and calculation to formal proof. This resource serves as a practical learning tool for mastering circle geometry and deductive reasoning within mathematics.","Circle Theorems: The alternate segment theorem  \nMaths  \nMr Chan  \nCircle Theorems: The alternate segment theorem  \n1. Shade in the angle that chord AC makes with tangent GH.  \n2. Shade in the angle subtended by the chord AC at the circumference.  \n3. Work out the size of each angle marked with a letter.  \nGive a reason for your answers.  \na) b)  \nc) d)  \nCircle Theorems: The alternate segment theorem  \n4. Work out the size of each angle. Give reasons for your answers.  \n5. Prove the alternate segment theorem.  \nCircle Theorems: The alternate segment theorem  \n1. Shade in the angle that chord AC makes with tangent GH.  \n2. Shade in the angle subtended by the chord AC at the circumference.  \n3. Work out the size of each angle marked with a letter.  \nGive a reason for your answers.  \na) b)  \nc) d)  \nThe alternate segment theorem.  \nCircle Theorems: The alternate segment theorem  \n4. Work out the size of each angle.  \nfor your answers.  \nGive reasons a)  \nb)  \nThe alternate segment theorem.  \nThe alternate segment theorem and angles ina triangle add up to 180º.  \n5. Prove the alternate segment theorem.","cbCaiqcdghYWjWWE","https://ap.wps.com/l/cbCaiqcdghYWjWWE","pdf",385692,1,6,"English","en",105,"# Circle Theorems: The Alternate Segment Theorem\n## Exercises\n### Problem 1: Shading angles\n### Problem 3: Calculating angles\n### Problem 4: Calculating angles and providing reasons\n### Problem 5: Proving the alternate segment theorem","[{\"question\":\"What is the main topic of this document?\",\"answer\":\"The main topic of this document is the Alternate Segment Theorem, a theorem in circle geometry.\"},{\"question\":\"What are the learning objectives for students using this material?\",\"answer\":\"Students are expected to be able to identify and shade specific angles, calculate the size of angles using geometric principles, and prove the Alternate Segment Theorem.\"},{\"question\":\"What additional geometric principle is mentioned in relation to the Alternate Segment Theorem?\",\"answer\":\"It is mentioned that angles in a triangle add up to 180 degrees, which is a principle relevant to understanding and proving circle theorems.\"}]","Circle Theorems: The Alternate Segment Theorem | PDF",1788601123,15,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":28},"circle-theorems-the-alternate-segment-theorem","",{"@graph":36,"@context":84},[37,53,67],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/circle-theorems-the-alternate-segment-theorem/207783/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What is the main topic of this document?","Question",{"text":74,"@type":75},"The main topic of this document is the Alternate Segment Theorem, a theorem in circle geometry.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What are the learning objectives for students using this material?",{"text":79,"@type":75},"Students are expected to be able to identify and shade specific angles, calculate the size of angles using geometric principles, and prove the Alternate Segment Theorem.",{"name":81,"@type":72,"acceptedAnswer":82},"What additional geometric principle is mentioned in relation to the Alternate Segment Theorem?",{"text":83,"@type":75},"It is mentioned that angles in a triangle add up to 180 degrees, which is a principle relevant to understanding and proving circle theorems.","https://schema.org",{"og:url":52,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,103,108,112,117,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":101,"slug":102},70,"exam",{"id":104,"doc_module":4,"doc_module_name":46,"category_name":105,"show_sort_weight":106,"slug":107},5,"Comic",60,"comic",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},"Technology",50,"technology",{"id":113,"doc_module":4,"doc_module_name":46,"category_name":114,"show_sort_weight":115,"slug":116},7,"Healthcare",40,"healthcare",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":119,"show_sort_weight":120,"slug":121},8,"Research & Report",30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":104,"slug":137},19,"General","general"]