{"id":18798,"date":"2018-01-18T11:50:31","date_gmt":"2018-01-18T11:50:31","guid":{"rendered":"https:\/\/cbselibrary.com\/?p=18798"},"modified":"2020-11-26T12:08:44","modified_gmt":"2020-11-26T06:38:44","slug":"math-labs-activity-angles-subtended-two-chords","status":"publish","type":"post","link":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/","title":{"rendered":"Math Labs with Activity – Angles Subtended by Two Chords"},"content":{"rendered":"

Math Labs with Activity – Angles Subtended by Two Chords<\/strong><\/span><\/h2>\n

OBJECTIVE<\/strong><\/span><\/p>\n

To verify that if the angles subtended by two chords at the centre of a circle are equal then the chords are equal<\/p>\n

Materials Required<\/strong><\/span><\/p>\n

    \n
  1. A sheet of white paper<\/li>\n
  2. A piece of cardboard<\/li>\n
  3. A sheet of tracing paper<\/li>\n
  4. A geometry box<\/li>\n
  5. A tube of glue<\/li>\n<\/ol>\n

    Theorem<\/strong><\/span>
    \nThe theorem to be verified is the converse of the theorem verified in Activity 15.
    \nThe theorem can be proved as below.
    \nConsider a circle with radius r and centre O having two chords AB and PQ such that \u2220AOB = \u2220POQ (see Figure 16.1).
    \n\"Math
    \nIn \u0394AOB and POQ, we have<\/p>\n

      \n
    1. AO = OP (each equal to r)<\/li>\n
    2. BO = OQ (each equal to r)<\/li>\n
    3. \u2220AOB = \u2220POQ (given)<\/li>\n<\/ol>\n

      Then, \u0394AOB is congruent to \u0394POQ (by SSA-criterion).
      \n\u2234<\/strong> AB = PQ.<\/p>\n

      Procedure<\/strong> <\/span>
      \nStep 1:<\/strong> Paste the sheet of white paper on the cardboard and mark a point O on this paper. With O as centre, draw a circle with any radius.
      \nStep 2:<\/strong> Draw two equal angles at the centre O of the circle.
      \n(This may be done using a pair of compasses as you have already learnt in the lower classes). Let these two angles be subtended by arcs Fig. 16.2.
      \nAB and PQ as shown in Figure 16.2. Join AB and PQ.
      \n\"Math
      \nStep 3:<\/strong> Trace the \u0394AOB on the tracing paper.
      \nStep 4:<\/strong> Place the \u0394AOB obtained on the tracing paper over the \u0394POQ such that \u2220AOB is superimposed over \u2220POQ.<\/p>\n

      Observations<\/strong><\/span>
      \nWe observe that \u0394AOB completely overlaps \u0394POQ. Therefore, \u0394AOB is congruent to \u0394POQ.
      \nSo, we conclude that the chord AB is equal to the chord PQ.<\/p>\n

      Result<\/strong> <\/span>
      \nIt is verified that if the angles subtended by two chords at the centre of a circle are equal then the chords are equal.<\/p>\n

      Math Labs with Activity<\/a>Math Labs<\/a>Science Practical Skills<\/a>Science Labs<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

      Math Labs with Activity – Angles Subtended by Two Chords OBJECTIVE To verify that if the angles subtended by two chords at the centre of a circle are equal then the chords are equal Materials Required A sheet of white paper A piece of cardboard A sheet of tracing paper A geometry box A tube … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6805],"tags":[],"yoast_head":"\nMath Labs with Activity - Angles Subtended by Two Chords - CBSE Library<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Math Labs with Activity - Angles Subtended by Two Chords\" \/>\n<meta property=\"og:description\" content=\"Math Labs with Activity – Angles Subtended by Two Chords OBJECTIVE To verify that if the angles subtended by two chords at the centre of a circle are equal then the chords are equal Materials Required A sheet of white paper A piece of cardboard A sheet of tracing paper A geometry box A tube ... Read more\" \/>\n<meta property=\"og:url\" content=\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/\" \/>\n<meta property=\"og:site_name\" content=\"CBSE Library\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/aplustopper\/\" \/>\n<meta property=\"article:published_time\" content=\"2018-01-18T11:50:31+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-11-26T06:38:44+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Angles-Subtended-by-Two-Chords-1.png\" \/>\n<meta name=\"twitter:card\" content=\"summary\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Prasanna\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/cbselibrary.com\/#organization\",\"name\":\"Aplus Topper\",\"url\":\"https:\/\/cbselibrary.com\/\",\"sameAs\":[\"https:\/\/www.facebook.com\/aplustopper\/\"],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/cbselibrary.com\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"contentUrl\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg\",\"width\":1585,\"height\":375,\"caption\":\"Aplus Topper\"},\"image\":{\"@id\":\"https:\/\/cbselibrary.com\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/cbselibrary.com\/#website\",\"url\":\"https:\/\/cbselibrary.com\/\",\"name\":\"CBSE Library\",\"description\":\"Improve your Grades\",\"publisher\":{\"@id\":\"https:\/\/cbselibrary.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/cbselibrary.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Angles-Subtended-by-Two-Chords-1.png\",\"contentUrl\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Angles-Subtended-by-Two-Chords-1.png\",\"width\":183,\"height\":196,\"caption\":\"Math Labs with Activity - Angles Subtended by Two Chords 1\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#webpage\",\"url\":\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/\",\"name\":\"Math Labs with Activity - Angles Subtended by Two Chords - CBSE Library\",\"isPartOf\":{\"@id\":\"https:\/\/cbselibrary.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#primaryimage\"},\"datePublished\":\"2018-01-18T11:50:31+00:00\",\"dateModified\":\"2020-11-26T06:38:44+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/cbselibrary.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Math Labs with Activity – Angles Subtended by Two Chords\"}]},{\"@type\":\"Article\",\"@id\":\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#webpage\"},\"author\":{\"@id\":\"https:\/\/cbselibrary.com\/#\/schema\/person\/2533e4338ba14fc0e4001efcca2f8794\"},\"headline\":\"Math Labs with Activity – Angles Subtended by Two Chords\",\"datePublished\":\"2018-01-18T11:50:31+00:00\",\"dateModified\":\"2020-11-26T06:38:44+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#webpage\"},\"wordCount\":307,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/cbselibrary.com\/#organization\"},\"image\":{\"@id\":\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Angles-Subtended-by-Two-Chords-1.png\",\"articleSection\":[\"CBSE\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#respond\"]}]},{\"@type\":\"Person\",\"@id\":\"https:\/\/cbselibrary.com\/#\/schema\/person\/2533e4338ba14fc0e4001efcca2f8794\",\"name\":\"Prasanna\",\"image\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/cbselibrary.com\/#personlogo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g\",\"caption\":\"Prasanna\"},\"url\":\"https:\/\/cbselibrary.com\/author\/prasanna\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Math Labs with Activity - Angles Subtended by Two Chords - CBSE Library","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/","og_locale":"en_US","og_type":"article","og_title":"Math Labs with Activity - Angles Subtended by Two Chords","og_description":"Math Labs with Activity – Angles Subtended by Two Chords OBJECTIVE To verify that if the angles subtended by two chords at the centre of a circle are equal then the chords are equal Materials Required A sheet of white paper A piece of cardboard A sheet of tracing paper A geometry box A tube ... Read more","og_url":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/","og_site_name":"CBSE Library","article_publisher":"https:\/\/www.facebook.com\/aplustopper\/","article_published_time":"2018-01-18T11:50:31+00:00","article_modified_time":"2020-11-26T06:38:44+00:00","og_image":[{"url":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Angles-Subtended-by-Two-Chords-1.png"}],"twitter_card":"summary","twitter_misc":{"Written by":"Prasanna","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/cbselibrary.com\/#organization","name":"Aplus Topper","url":"https:\/\/cbselibrary.com\/","sameAs":["https:\/\/www.facebook.com\/aplustopper\/"],"logo":{"@type":"ImageObject","@id":"https:\/\/cbselibrary.com\/#logo","inLanguage":"en-US","url":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","contentUrl":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","width":1585,"height":375,"caption":"Aplus Topper"},"image":{"@id":"https:\/\/cbselibrary.com\/#logo"}},{"@type":"WebSite","@id":"https:\/\/cbselibrary.com\/#website","url":"https:\/\/cbselibrary.com\/","name":"CBSE Library","description":"Improve your Grades","publisher":{"@id":"https:\/\/cbselibrary.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/cbselibrary.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#primaryimage","inLanguage":"en-US","url":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Angles-Subtended-by-Two-Chords-1.png","contentUrl":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Angles-Subtended-by-Two-Chords-1.png","width":183,"height":196,"caption":"Math Labs with Activity - Angles Subtended by Two Chords 1"},{"@type":"WebPage","@id":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#webpage","url":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/","name":"Math Labs with Activity - Angles Subtended by Two Chords - CBSE Library","isPartOf":{"@id":"https:\/\/cbselibrary.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#primaryimage"},"datePublished":"2018-01-18T11:50:31+00:00","dateModified":"2020-11-26T06:38:44+00:00","breadcrumb":{"@id":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/cbselibrary.com\/"},{"@type":"ListItem","position":2,"name":"Math Labs with Activity – Angles Subtended by Two Chords"}]},{"@type":"Article","@id":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#article","isPartOf":{"@id":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#webpage"},"author":{"@id":"https:\/\/cbselibrary.com\/#\/schema\/person\/2533e4338ba14fc0e4001efcca2f8794"},"headline":"Math Labs with Activity – Angles Subtended by Two Chords","datePublished":"2018-01-18T11:50:31+00:00","dateModified":"2020-11-26T06:38:44+00:00","mainEntityOfPage":{"@id":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#webpage"},"wordCount":307,"commentCount":0,"publisher":{"@id":"https:\/\/cbselibrary.com\/#organization"},"image":{"@id":"https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#primaryimage"},"thumbnailUrl":"https:\/\/cbselibrary.com\/wp-content\/uploads\/2018\/01\/Math-Labs-with-Activity-Angles-Subtended-by-Two-Chords-1.png","articleSection":["CBSE"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/cbselibrary.com\/math-labs-activity-angles-subtended-two-chords\/#respond"]}]},{"@type":"Person","@id":"https:\/\/cbselibrary.com\/#\/schema\/person\/2533e4338ba14fc0e4001efcca2f8794","name":"Prasanna","image":{"@type":"ImageObject","@id":"https:\/\/cbselibrary.com\/#personlogo","inLanguage":"en-US","url":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/174540ad43736c7d1a4c4f83c775e74d?s=96&d=mm&r=g","caption":"Prasanna"},"url":"https:\/\/cbselibrary.com\/author\/prasanna\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/posts\/18798"}],"collection":[{"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/comments?post=18798"}],"version-history":[{"count":0,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/posts\/18798\/revisions"}],"wp:attachment":[{"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/media?parent=18798"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/categories?post=18798"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cbselibrary.com\/wp-json\/wp\/v2\/tags?post=18798"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}