{"id":3225,"date":"2022-01-05T19:32:00","date_gmt":"2022-01-05T19:32:00","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=3225"},"modified":"2022-03-03T15:10:36","modified_gmt":"2022-03-03T15:10:36","slug":"parallel-lines-and-transversals","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/parallel-lines-and-transversals\/","title":{"rendered":"Parallel lines and Transversals"},"content":{"rendered":"[vc_section full_width=&#8221;stretch_row&#8221; content_placement=&#8221;middle&#8221; css=&#8221;.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;}&#8221; el_id=&#8221;bg-sec&#8221;][vc_row full_width=&#8221;stretch_row_content&#8221; el_class=&#8221;faaaq&#8221;][vc_column width=&#8221;1\/12&#8243;][\/vc_column][vc_column width=&#8221;1\/2&#8243;][vc_row_inner content_placement=&#8221;middle&#8221; el_class=&#8221;topheadingg&#8221;][vc_column_inner width=&#8221;1\/6&#8243;][vc_single_image image=&#8221;2283&#8243; img_size=&#8221;full&#8221;][\/vc_column_inner][vc_column_inner width=&#8221;5\/6&#8243;][vc_column_text]\n<h1>Parallel lines and Transversals<\/h1>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=&#8221;headingnew&#8221;]Concept[\/vc_column_text][vc_column_text]Calculate the missing angle, provided a pair of parallel lines, two transversals, and one or two angle measures.[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Rules[\/vc_column_text][vc_column_text]Use the properties of the following angles to find the value of the <a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/finding-angle-measures\">missing angle.<\/a><\/p>\n<p>Complementary angles are two angles that together form a right angle.\u200b The sum of two complementary angles is 90 degrees. \u200bTo find the missing complementary angle, subtract the given angle from 90 degrees.<\/p>\n<p>Supplementary angles are two angles that together form a straight angle.\u200b The sum of two supplementary angles is 180 degrees. \u200bTo find the missing supplementary angle, subtract the given angle from 180 degrees.<\/p>\n<p>Alternate interior angles are on opposite sides of the transversal and between the parallel lines.<\/p>\n<p>Alternate exterior angles are on opposite sides of the transversal and on the outside of the parallel lines.<\/p>\n<p>Corresponding angles are in the same position relative to the transversal and each of the parallel lines.[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">In the figure, lines b and c are parallel, and line a is perpendicular to line b. Find the measure of angle 4.<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/lines\"><img loading=\"lazy\" class=\"alignnone wp-image-3227 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/1-26.png\" alt=\"\" width=\"228\" height=\"192\" \/><\/a>[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Solution[\/vc_column_text][vc_column_text]Since a and b are perpendicular, angle 1 measures 90 degrees. Since b and c are parallel, angles 1 and 2 are corresponding angles. So, angle 2 measures 90 degrees as well. Angle 3 and 4 together add up to 90 degrees and angle 3 is a vertical angle to the 40 degree angle, so angle 4 equals <span style=\"color: #ff0000;\">50 degrees<\/span>[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Practice Parallel lines and Transversals[\/vc_column_text][vc_row_inner el_class=&#8221;boxxborder&#8221;][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 shows alternate interior angles?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/lines\"><img loading=\"lazy\" class=\"alignnone wp-image-3235 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/11-17.png\" alt=\" Parallel lines and Transversals - Practice Problem 1\" width=\"275\" height=\"308\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/11-17.png 275w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/11-17-268x300.png 268w\" sizes=\"(max-width: 275px) 100vw, 275px\" \/><\/a><\/p>\n<p>&nbsp;<\/p>\n[\/vc_column_text][vc_single_image image=&#8221;2159&#8243; img_size=&#8221;full&#8221; alignment=&#8221;right&#8221; onclick=&#8221;custom_link&#8221; link=&#8221;https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/lines&#8221;][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=&#8221;30px&#8221;][vc_row_inner el_class=&#8221;boxxborder&#8221;][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 figure, lines c and d are parallel. Find the measure of angle 3. <\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/lines\"><img loading=\"lazy\" class=\"alignnone wp-image-3233 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/12-11.png\" alt=\" Parallel lines and Transversals - Practice Problem 2\" width=\"310\" height=\"337\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/12-11.png 310w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/12-11-276x300.png 276w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=&#8221;2159&#8243; img_size=&#8221;full&#8221; alignment=&#8221;right&#8221; onclick=&#8221;custom_link&#8221; link=&#8221;https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/lines&#8221;][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=&#8221;30px&#8221;][vc_row_inner el_class=&#8221;boxxborder&#8221;][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">Handrails on a staircase must be constructed parallel to each other to ensure the support of the rail. Knowing this, what is the value of x? <\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/lines\"><img loading=\"lazy\" class=\"alignnone wp-image-3231 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/13-9.png\" alt=\" Parallel lines and Transversals - Practice Problem 3\" width=\"176\" height=\"345\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/13-9.png 176w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/13-9-153x300.png 153w\" sizes=\"(max-width: 176px) 100vw, 176px\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=&#8221;2159&#8243; img_size=&#8221;full&#8221; alignment=&#8221;right&#8221; onclick=&#8221;custom_link&#8221; link=&#8221;https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/lines&#8221;][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=&#8221;30px&#8221;][\/vc_column][vc_column width=&#8221;1\/3&#8243; css=&#8221;.vc_custom_1633369011398{margin-bottom: 50px !important;}&#8221;][vc_row_inner el_class=&#8221;stickynotee&#8221;][vc_column_inner][vc_single_image image=&#8221;2265&#8243; img_size=&#8221;full&#8221; alignment=&#8221;center&#8221; css_animation=&#8221;fadeIn&#8221; css=&#8221;.vc_custom_1633509989314{border-radius: 10px !important;}&#8221; el_class=&#8221;stickypin&#8221;][vc_column_text]<strong>Parallel lines<\/strong> are two or more lines that never intersect.<\/p>\n<p><strong>Perpendicular lines<\/strong> are two lines that intersect at a right angle.<\/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>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>Corresponding angles<\/strong> are in the same position relative to the transversal and each of the parallel lines.<\/p>\n<p><strong>Vertical angles<\/strong> are a pair of opposite angles formed by intersecting lines. Vertical angles are always congruent.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=&#8221;boxxborder2&#8243;]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><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\/7th-grade\/finding-angle-measures\"><span style=\"color: #ed5600;\">Finding Angle Measures<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/angle-relationships\"><span style=\"color: #ed5600;\">Angle Relationships<\/span><\/a>[\/vc_column_text][vc_column_text el_class=&#8221;boxxborder2&#8243; css=&#8221;.vc_custom_1635245091562{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;}&#8221;]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/congruent-lines\"><span style=\"color: #333399;\">Congruent Lines<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/classify-quadrilaterals\"><span style=\"color: #333399;\">Classify Quadrilaterals<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/quadrilateral-facts\"><span style=\"color: #333399;\">Quadrilateral Facts<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/geometric-proof\"><span style=\"color: #333399;\">Geometric Proof<\/span><\/a>[\/vc_column_text][vc_row_inner equal_height=&#8221;yes&#8221; 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content_placement=&#8221;middle&#8221; css=&#8221;.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;}&#8221; el_id=&#8221;bg-sec&#8221;][vc_row full_width=&#8221;stretch_row_content&#8221; el_class=&#8221;faaaq&#8221;][vc_column width=&#8221;1\/12&#8243;][\/vc_column][vc_column width=&#8221;1\/2&#8243;][vc_row_inner content_placement=&#8221;middle&#8221; el_class=&#8221;topheadingg&#8221;][vc_column_inner width=&#8221;1\/6&#8243;][vc_single_image image=&#8221;2283&#8243; img_size=&#8221;full&#8221;][\/vc_column_inner][vc_column_inner width=&#8221;5\/6&#8243;][vc_column_text] Parallel lines and Transversals [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=&#8221;headingnew&#8221;]Concept[\/vc_column_text][vc_column_text]Calculate the missing angle, provided a pair of parallel lines, two transversals, and one or two angle measures.[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Rules[\/vc_column_text][vc_column_text]Use the properties of the following angles to find [&hellip;]<\/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>Parallel lines and Transversals | Oryx Learning<\/title>\n<meta name=\"description\" content=\"Parallel lines refer to lines that are always at the same distance from each other and never cross. 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