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It lists core terms for sets, angles, triangles, polygons, parallel lines, and circle geometry, then summarizes important theorems such as vertically-opposite angles, isosceles triangle properties, alternate/corresponding angles, triangle angle sum, exterior angle relationships, triangle inequality, parallelogram and diagonal properties, and key circle and Pythagoras results.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/paper-templates/","Paper 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terminology?","Question",{"text":62,"@type":63},"Definitions are set out in the syllabus and, while memorizing every definition is not required, students are expected to use the terms accurately in ordinary language, supported by informal remarks.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"Which theorem states that vertically opposite angles are equal?",{"text":67,"@type":63},"Theorem 1 (Vertically-opposite Angles) states that vertically opposite angles are equal in measure.",{"name":69,"@type":60,"acceptedAnswer":70},"What does the Pythagoras theorem say for a right-angled triangle?",{"text":71,"@type":63},"Theorem 14 (Pythagoras) states that in a right-angle triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},573389,1792053101,{"code":4,"msg":81,"data":82},"success",[83,88,93,98,103,108,113,118,122],{"id":84,"doc_module":22,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},11,"Presentations",90,"presentations",{"id":89,"doc_module":22,"doc_module_name":25,"category_name":90,"show_sort_weight":91,"slug":92},12,"Resumes",80,"resumes",{"id":94,"doc_module":22,"doc_module_name":25,"category_name":95,"show_sort_weight":96,"slug":97},14,"Invoices",70,"invoices",{"id":99,"doc_module":22,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},15,"Posters",60,"posters",{"id":104,"doc_module":22,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},16,"Social 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of the Terminology for the Geometrical Concepts  \nEach of the following is set out in the syllabus and whilst there is no need to learn all the definitions off by heart you are expected to be able to use ordinary language, supplemented by informal remarks to define the terms.  \nConcepts  \n• set,  \n• subset,  \n• plane,  \n• point,  \n• line,  \n• ray,  \n• angle,  \n• real number,  \n• length,  \n• degree,  \n• triangle,  \n• right-angle,  \n• congruent triangles,• similar triangles,• parallel lines,  \n• parallelogram,  \n• area,  \n• segment,  \n• collinear points,• distance,  \n• midpoint of a segment,  \n• reflex angle,  \n• ordinary angle,  \n• straight angle,  \n• null angle,  \n• full angle,  \n• supplementary angles,• vertically-opposite angles,• acute angle,  \n• obtuse angle,  \n• angle bisector,  \n• perpendicular lines,  \n• perpendicular bisector of a segment,  \n• ratio,  \n• isosceles triangle,  \n• equilateral triangle,  \n• scalene triangle,  \n• right-angled triangle,• exterior angles of a triangle,• interior opposite angles,• hypotenuse,  \n• alternate angles,  \n• corresponding angles,  \n• polygon,  \n• quadrilateral,  \n• convex quadrilateral,• rectangle,  \n• square,  \n• rhombus,  \n• base and corresponding apex and height of triangle or parallelogram,  \n• transversal line,  \n• circle,  \n• centre of a circle,  \n• radius,  \n• diameter,  \n• chord,  \n• arc,  \n• sector,  \n• circumference of a circle,• disc,  \n• area of a disc,  \n• circumcircle,  \n• tangent to a circle,  \n• point of contact of a tangent,  \n• vertex,  \n• vertices (of angle, triangle, polygon),  \n• endpoints of segment,• arms of an angle,  \n• equal segments,  \n• equal angles,  \n• adjacent sides,  \n• angles,  \n• or vertices of triangles or quadrilaterals,  \n• the side opposite an angle of a triangle,  \n• opposite sides or angles of a quadrilateral.  \n[www.mathspoints.ie](www.mathspoints.ie)  \n\n| Geometry – Leaving Cert Ordinary Level Revision Sheet\u003Cbr>|  |\n| --- | --- |\n| A theorem is a statement deduced from the axioms by logical argument. At Ordinary level none of these theorems need to be proved formally, though all are studied, and a knowledge of all of them is necessary so as to solve questions in any geometry section. |  |\n| Theorems\u003Cbr>Theorem 1 (Vertically-opposite Angles)\u003Cbr>Vertically opposite angles are equal in measure.\u003Cbr>Theorem 2 (Isosceles Triangles)\u003Cbr>In an isosceles triangle the angles opposite the equal sides are equal.\u003Cbr>Conversely, if two angles are equal, then the triangle is isosceles.\u003Cbr>Theorem 3 (Alternate Angles)\u003Cbr>If a transversal makes equal alternate angles on two lines, then the lines are parallel.\u003Cbr>Conversely, if two lines are parallel, then any transversal will make equal alternate angles with them.\u003Cbr>Theorem 4 (Angle Sum 180)\u003Cbr>The angles in any triangle add to 180° .\u003Cbr>Theorem 5 (Corresponding Angles)\u003Cbr>Two lines are parallel if and only if for any transversal, corresponding angles are equal.\u003Cbr>Theorem 6 (Exterior Angle)\u003Cbr>Each exterior angle of a triangle is equal to the sum of the interior opposite angles.\u003Cbr>Theorem 7\u003Cbr>The angle opposite the greater of two sides is greater than the angle opposite the lesser side.\u003Cbr>Conversely, the side opposite the greater of two angles is greater than the side opposite the lesser angle.\u003Cbr>Theorem 8 (Triangle Inequality)\u003Cbr>Two sides ofa triangle are together greater than the third.\u003Cbr>Theorem 9\u003Cbr>In a parallelogram, opposite sides are equal, and opposite angles are equal.\u003Cbr>Converse 1 to Theorem 9:\u003Cbr>If the opposite angles of a convex quadrilateral are equal, then it is a parallelogram.\u003Cbr>Converse 2 to Theorem 9:\u003Cbr>If the opposite sides of a convex quadrilateral are equal, then it is a parallelogram.\u003Cbr>Theorem 10\u003Cbr>The diagonals ofa parallelogram bisect one another. | Theorem 11\u003Cbr>If three parallel lines cut off equal segments on some transversal line, then they will cut off equal segments on any other transversal.\u003Cbr>Theorem 12\u003Cbr>Let ∆ABC be a triangle. If a line l is parallel to B","cbCaicTVTiBWoiUU","https://ap.wps.com/l/cbCaicTVTiBWoiUU","pdf",336826,9,"English","# Key Terminology\n## Theorems (Ordinary Level)\n## Additional Geometry Definitions (Logic and Proofs)","[{\"question\":\"What is expected when learning the geometry terminology?\",\"answer\":\"Definitions are set out in the syllabus and, while memorizing every definition is not required, students are expected to use the terms accurately in ordinary language, supported by informal remarks.\"},{\"question\":\"Which theorem states that vertically opposite angles are equal?\",\"answer\":\"Theorem 1 (Vertically-opposite Angles) states that vertically opposite angles are equal in measure.\"},{\"question\":\"What does the Pythagoras theorem say for a right-angled triangle?\",\"answer\":\"Theorem 14 (Pythagoras) states that in a right-angle triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.\"}]","Geometry - Revision Sheet - Theorems and Key Definitions | PDF",1791938830]