{"id":4094,"date":"2022-01-30T08:21:57","date_gmt":"2022-01-30T08:21:57","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=4094"},"modified":"2022-03-01T17:30:48","modified_gmt":"2022-03-01T17:30:48","slug":"geometry-proofs","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/geometry-proofs\/","title":{"rendered":"Geometry Proofs"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>Geometry Proofs<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Geometric proofs are given statements that prove a mathematical concept is true. In order for a proof to be proven true, it has to include multiple steps. These steps are made up of reasons and statements.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]<strong>1. <a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof\">Paragraph proof<\/a><br \/>\n<\/strong>Paragraph proofs are comprehensive paragraphs that explain the process of each proof. Like two-column proofs, they have multiple steps and justifications. But instead of columns, the given information is formatted like a word problem \u2014 written out in long-hand format.<\/p>\n<p>Paragraph proofs need to be written in chronological order, showing that each step allows the next statement to be true. Each step needs to be supported by a definition, theorem, or postulate.<\/p>\n<p><strong>2. <a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof\">Two-column proof<\/a><br \/>\n<\/strong>In two-column proofs, the first column has a chronological list of steps. The second column uses deductive reasoning to create a complementary justification for each step. These justifications are either definitions, postulates (assumptions based on mathematical reasoning), or theorems (rules demonstrated through formulas).<\/p>\n<p>1. Start with the given information.<br \/>\n2. Statements with the same reason can be combined into one step.<br \/>\n3 You must have a reason for EVERY statement.<br \/>\n4. The order of the statements in the proof is not always fixed, but make sure the order makes logical sense.<br \/>\n5. Reasons will be definitions, postulates, properties and previously proven theorems. \u201cGiven\u201d is only used as a reason if the information in the statement column was given in the problem.<br \/>\n6. Use symbols and abbreviations for words within proofs.[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">Complete the two-column proof<\/span><\/strong><br \/>\n<strong>Given: Lines s and n are parallel and cut by transversal t.<\/strong><br \/>\n<strong>Prove: \u22201 and \u22204 are supplementary<\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof\"><img loading=\"lazy\" class=\"alignnone \" style=\"margin-top: 10px;\" src=\"https:\/\/cdn.oryxlearning.com\/media_assets\/1638360776248.svg\" width=\"164\" height=\"199\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-4096 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/5-10-e1638340353712.png\" alt=\"\" width=\"342\" height=\"302\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/5-10-e1638340353712.png 342w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/5-10-e1638340353712-300x265.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/a>[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]Use the linear pairs to establish a relationship of supplementary angles. Linear pairs are supplementary angles that share a line that forms one of the sides of each angle. Then, use the fact that corresponding angles from the parallel lines are congruent to relate angles 1 and 4.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof\"><img loading=\"lazy\" class=\"alignnone wp-image-4098 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/6-2.png\" alt=\"\" width=\"343\" height=\"328\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/6-2.png 343w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/6-2-300x287.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/a>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice Geometry Proofs[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">Which pair of angles represent corresponding angles? <\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof\"><img loading=\"lazy\" class=\"alignnone wp-image-4100 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/7-1.png\" alt=\" Geometry Proofs Examples - Practice Problem 1\" width=\"297\" height=\"398\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/7-1.png 297w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/7-1-224x300.png 224w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">In the diagram, lines a and b intersect. Choose the reason for the statement.<br \/>\nm\u22202 = m\u22204 because:<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof\"><img loading=\"lazy\" class=\"alignnone wp-image-4102 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/8-1.png\" alt=\" Geometry Proofs Examples - Practice Problem 2\" width=\"276\" height=\"539\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/8-1.png 276w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/8-1-154x300.png 154w\" sizes=\"(max-width: 276px) 100vw, 276px\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">In the diagram \u2220ABD \u2248 \u2220EFH, \u2220CBD is the complement of \u2220ABD and \u2220GHF is the complement of \u2220EFH<br \/>\nComplete the paragraph proof to show that \u2220CBD \u2245 \u2220GHF.<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof\"><img loading=\"lazy\" class=\"alignnone wp-image-4105 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/9-1.png\" alt=\" Geometry Proofs Examples - Practice Problem 3\" width=\"392\" height=\"431\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/9-1.png 392w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/9-1-273x300.png 273w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 4<\/h5>\n<p><strong><span style=\"color: #16a085;\">Given: \u22204\u2245\u22203;c\u2225d<br \/>\nProve: \u22204\u2245\u22202 <\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof\"><img loading=\"lazy\" class=\"alignnone wp-image-4107 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-1.png\" alt=\" Geometry Proofs Examples - Practice Problem 4\" width=\"459\" height=\"402\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-1.png 459w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-1-300x263.png 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]<strong>Parallel lines<\/strong> are two or more lines that never intersect.<\/p>\n<p><strong>Transversal line<\/strong> is a line that passes through two lines in the same plane at two distinct points.<\/p>\n<p><strong>Corresponding angles<\/strong> are in the same position relative to the transversal and each of the parallel lines.<\/p>\n<p><strong>Alternate interior angles<\/strong> are on opposite sides of the transversal and between the parallel lines.<\/p>\n<p><strong>Alternate exterior angles<\/strong> are on opposite sides of the transversal and on the outside of the parallel lines.<\/p>\n<p><strong>Linear pair:<\/strong> Two adjacent angles whose noncommon sides form a line are a linear pair. The sum of the measures of the angles in a linear pair is 180 degrees.\u200b<\/p>\n<p><strong>Vertical angles<\/strong> are two angles that are formed by intersecting lines. They are not adjacent but share a vertex. Vertical angles have the same measure.\u200b<\/p>\n<p><strong>Complementary angles<\/strong> – two angles whose sum is 90 degrees.<\/p>\n<p><strong>Supplementary angles<\/strong> – two angles whose sum is 180 degrees.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/angle-relationships\"><span style=\"color: #ed5600;\">Angle Relationships<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/complementary-and-supplementary-angles\"><span style=\"color: #ed5600;\">Complementary and Supplementary Angles<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/lines\"><span style=\"color: #ed5600;\">Lines<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1635315769698{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/angles-of-a-triangle\"><span style=\"color: #333399;\">Angles of a Triangle<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/polygons-and-angles\"><span style=\"color: #333399;\">Polygons and Angles<\/span><\/a>[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||”][vc_btn title=”Grade 4″ color=”blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F4th-grade%2Fmaths|title:Grade%204%20Math||”][vc_btn title=”Grade 5″ color=”green” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F5th-grade%2Fmaths|title:Grade%205%20Math||”][vc_btn title=”Grade 6″ color=”info” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F6th-grade%2Fmaths|title:Grade%206%20Math||”][vc_btn title=”Grade 7″ color=”vista-blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F7th-grade%2Fmaths|title:Grade%207%20Math||”][vc_btn title=”Grade 8″ color=”mulled-wine” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F8th-grade%2Fmaths|title:Grade%208%20Math||”][\/vc_column_inner][\/vc_row_inner][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Geometry and Spatial sense” color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Fgeometry-and-spatial-sense|title:Geometry%20and%20Spatial%20sense||”][vc_btn title=”Graphs” color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Fgraphs|title:Graphs||”][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] Geometry Proofs [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]Geometric proofs are given statements that prove a mathematical concept is true. In order for a proof to be proven true, it has to include multiple steps. These steps […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Geometry Proofs | Oryx Learning<\/title>\n<meta name=\"description\" content=\"Geometric proofs are given statements that prove a mathematical concept is true. In order for a proof to be proven true, it has to include multiple steps. 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