{"id":633,"date":"2012-01-31T15:50:37","date_gmt":"2012-01-31T15:50:37","guid":{"rendered":"https:\/\/schooltutoring.com\/scholarship\/?p=633"},"modified":"2014-12-02T08:33:49","modified_gmt":"2014-12-02T08:33:49","slug":"inscribed-angle-and-conjectures","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/01\/31\/inscribed-angle-and-conjectures\/","title":{"rendered":"Inscribed Angle and Conjectures"},"content":{"rendered":"<p>An <strong>inscribed angle<\/strong> is an angle formed by two chords in a circle which meet at a common point. This common endpoint forms the vertex of the inscribed angle. The other two endpoints of the chords define <strong>intercepted arc<\/strong> on the circle.<\/p>\n<p><a href=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/inscbed-angle.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-634\" src=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/inscbed-angle.png\" alt=\"\" width=\"193\" height=\"190\" \/><\/a><\/p>\n<p>In the figure above ABC is an inscribed angle and AC is an inscribed arc.<\/p>\n<p><strong>Conjecture 1: <\/strong>In a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc. (A central angle is any angle whose vertex is located at the center of a circle.)<\/p>\n<p><a href=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/inscrbd-conj1.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-635\" src=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/inscrbd-conj1.png\" alt=\"\" width=\"194\" height=\"186\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>angle ABC = 1\/2 \u00d7 angle AOC<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Conjecture 2:<\/strong> In a circle, two inscribed angles with the same intercepted arc are congruent.<\/p>\n<p><a href=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/inscrbd-conj2.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-637\" src=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/inscrbd-conj2.png\" alt=\"\" width=\"183\" height=\"174\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n<p>angle ABC = angleADC<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Conjecture 3: <\/strong>Any angle inscribed in a semi-circle is a right angle.<\/p>\n<p><a href=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/inscrbd-conj3.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-638\" src=\"https:\/\/schooltutoring.com\/wp-content\/uploads\/sites\/8\/inscrbd-conj3.png\" alt=\"\" width=\"210\" height=\"179\" \/><\/a><\/p>\n<p>angle ABC = 90\u00b0<\/p>\n<p>SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students, visit: <a href=\"https:\/\/schooltutoring.com\">SchoolTutoring Academy<\/a>..<\/p>\n","protected":false},"excerpt":{"rendered":"<p>An inscribed angle is an angle formed by two chords in a circle which meet at a common point. This common endpoint forms the vertex of the inscribed angle. The other two endpoints of the chords define intercepted arc on the circle. In the figure above ABC is an inscribed angle and AC is an [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[10],"tags":[943,1421],"class_list":["post-633","post","type-post","status-publish","format-standard","hentry","category-geometry","tag-inscribedangle","tag-propertiesofinscribedangle"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/633","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=633"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/633\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=633"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=633"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=633"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}