{"id":67,"date":"2026-08-05T05:58:41","date_gmt":"2026-08-05T05:58:41","guid":{"rendered":"https:\/\/sqoolpapers.co.za\/notes\/g\/"},"modified":"2026-08-22T16:08:09","modified_gmt":"2026-08-22T16:08:09","slug":"euclidean-geometry-g12-maths-t4p2","status":"publish","type":"post","link":"https:\/\/repstaq.com\/study-guide-docs\/euclidean-geometry-g12-maths-t4p2\/","title":{"rendered":"Euclidean Geometry-G12-Maths-T4P2"},"content":{"rendered":"\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Euclidean Geometry Study Notes<\/h2>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Circle geometry<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Circle geometry focuses on the properties and relationships involving circles, such as chords, tangents, diameters, radii, and angles in circles.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Important facts:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The radius is a line segment from the centre of the circle to any point on the circle.<\/li>\n\n\n\n<li>The diameter is a straight line passing through the centre, connecting two points on the circle, and is twice the radius.<\/li>\n\n\n\n<li>A chord is a segment joining any two points on the circle.<\/li>\n\n\n\n<li>An arc is a section of the circumference of a circle.<\/li>\n\n\n\n<li>The angle at the centre of the circle is twice the angle at the circumference subtended by the same arc.<\/li>\n\n\n\n<li>The perpendicular from the centre of the circle to a chord bisects the chord.<\/li>\n<\/ul>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: Given a circle with centre O, and chord AB = 6 units. If the perpendicular from O to AB meets AB at point M and OM = 2 units, find the radius of the circle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Write down what is given.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nAB = 6,quad OM = 2\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Draw a diagram with O, A, B, M.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 3: Since OM \u27c2 AB and M is the midpoint of AB,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nAM = MB = 3\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 4: Use Pythagoras&#8217; theorem in triangle OMA.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nOA^2 = OM^2 + AM^2\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 5: Substitute.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nOA^2 = 2^2 + 3^2\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nOA^2 = 4 + 9\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nOA^2 = 13\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nOA = sqrt{13}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 6: The radius is <span class=\"katex-eq\" data-katex-display=\"false\"> sqrt{13} <\/span> units.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Always mark the centre, radius, and any given angles or perpendiculars on your diagram.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common mistake: Forgetting that the perpendicular from the centre bisects the chord.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Tangents and chords<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A tangent is a straight line that touches a circle at exactly one point, called the point of contact. A chord is a line segment joining any two points on a circle.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Important facts:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A tangent to a circle is perpendicular to the radius at the point of contact.<\/li>\n\n\n\n<li>Tangents drawn from the same external point are equal in length.<\/li>\n\n\n\n<li>The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment of the circle (the tangent-chord theorem).<\/li>\n<\/ul>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: In the diagram, AB is a tangent to the circle at point A and AC is a chord. If <span class=\"katex-eq\" data-katex-display=\"false\"> AB = 8\\ units <\/span> and both AB and AD are tangents from point A, find the length of AD.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Tangents from the same external point are equal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nAB = AD = 8\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Final answer: <span class=\"katex-eq\" data-katex-display=\"false\"> AD = 8\\ units <\/span>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Use the tangent properties to establish lengths and relationships quickly.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common mistake: Confusing a secant (line intersecting the circle at two points) with a tangent.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/sqooltutors.co.za\/sign-up-b\/\"><img decoding=\"async\" src=\"https:\/\/lmxddlwowqlsyucleuyv.supabase.co\/storage\/v1\/object\/public\/pdf_ads\/batch%201\/Doc%20Image%20Aug%2022,%202026,%2004_21_49%20PM%20(1).png\" alt=\"\"\/><\/a><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Cyclic quadrilaterals<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Important facts:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The opposite angles of a cyclic quadrilateral add up to 180\u00b0.<\/li>\n\n\n\n<li>The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.<\/li>\n<\/ul>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: Given a cyclic quadrilateral ABCD, if angle A = 75\u00b0, find angle C.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Opposite angles in a cyclic quadrilateral are supplementary.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nangle A + angle C = 180^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Substitute <span class=\"katex-eq\" data-katex-display=\"false\"> angle A = 75^\\circ <\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n75^\\circ + angle C = 180^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nangle C = 180^\\circ - 75^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nangle C = 105^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common mistake: Only one pair of opposite angles must sum to 180\u00b0, but both pairs do.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Always check if all vertices are on the circle before using these properties.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Similar triangles<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Important facts:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>AA (Angle-Angle) criterion: Two triangles are similar if two pairs of corresponding angles are equal.<\/li>\n\n\n\n<li>Sides of similar triangles are in the same ratio.<\/li>\n\n\n\n<li>Corresponding heights and medians of similar triangles are also in the same ratio.<\/li>\n<\/ul>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: Triangle ABC is similar to triangle DEF, and <span class=\"katex-eq\" data-katex-display=\"false\"> AB = 4\\ units <\/span>, <span class=\"katex-eq\" data-katex-display=\"false\"> BC = 6\\ units <\/span>, <span class=\"katex-eq\" data-katex-display=\"false\"> DE = 8\\ units <\/span>. Find the length of EF.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Write the proportion.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\dfrac{AB}{DE} = \\dfrac{BC}{EF}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Substitute known values.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n\\dfrac{4}{8} = \\dfrac{6}{EF}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 3: Cross-multiply.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n4 \\times EF = 8 \\times 6\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\n4EF = 48\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nEF = \\dfrac{48}{4}\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nEF = 12\\ units\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common mistake: Not matching corresponding sides correctly.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Mark equal angles and set up side ratios correctly.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Congruent triangles<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Triangles are congruent if all their corresponding sides and angles are equal.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Important facts:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Three rules for congruency: SSS (side-side-side), SAS (side-angle-side), ASA (angle-side-angle).<\/li>\n\n\n\n<li>Congruent triangles are identical in shape and size and can be superimposed with each other.<\/li>\n\n\n\n<li>Proving triangles congruent allows you to conclude all corresponding parts (CPCTC: Corresponding Parts of Congruent Triangles are Congruent).<\/li>\n<\/ul>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: Prove that triangle ABC is congruent to triangle DEF if:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">AB = DE = 7 units,<br>BC = EF = 9 units,<br>AC = DF = 5 units<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: State the SSS rule.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If all three sides are equal, the triangles are congruent.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nAB = DE,\\ BC = EF,\\ AC = DF\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, triangle ABC \u2245 triangle DEF by SSS.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common mistake: Using AAA (Angle-Angle-Angle) for congruency \u2013 AAA only gives similarity, not congruency.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Midpoint theorem<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The midpoint theorem states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Important facts:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The line joining the midpoints of two sides of a triangle is called the midline.<\/li>\n\n\n\n<li>The midline is parallel to the third side.<\/li>\n\n\n\n<li>The midline is half the length of the third side.<\/li>\n<\/ul>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: In triangle ABC, D and E are midpoints of AB and AC. If BC = 10 units, find DE.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: By the midpoint theorem,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nDE = \\frac{1}{2} BC\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nDE = \\frac{1}{2} \\times 10\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nDE = 5\\ units\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: In coordinate geometry, use the midpoint formula for accuracy.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Worked coordinate geometry example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: Given points A(2, 3) and B(6, 7). Find the midpoint M.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Use the midpoint formula.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nM \\left( \\frac{x_1 + x_2}{2}, \\frac{y_1 + y_2}{2} \\right)\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Substitute values.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nM \\left( \\frac{2+6}{2}, \\frac{3+7}{2} \\right)\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nM(4, 5)\n<\/span><\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/sqooltutors.co.za\/sign-up-b\/\"><img decoding=\"async\" src=\"https:\/\/lmxddlwowqlsyucleuyv.supabase.co\/storage\/v1\/object\/public\/pdf_ads\/batch%201\/Doc%20Image%20Aug%2022,%202026,%2004_22_10%20PM%20(1).png\" alt=\"\"\/><\/a><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Riders and formal geometric proofs<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In Euclidean geometry, a &#8220;rider&#8221; refers to a deductive geometry problem, often requiring use of circle, triangle and quadrilateral properties. Formal geometric proofs involve logical application of theorems and axioms with clear reasons for each statement.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Important steps in formal geometric proofs:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw a clear, labelled diagram.<\/li>\n\n\n\n<li>Write known facts and what needs to be proved.<\/li>\n\n\n\n<li>List every step with an appropriate reason (theorem, axiom, or definition).<\/li>\n\n\n\n<li>Use standard notation and terminology.<\/li>\n<\/ul>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Example<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Question: In circle O, AB is a diameter. Prove that angle ACB = 90\u00b0 if C lies on the circle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 1: Statement: AB is a diameter (given).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Step 2: Angle subtended by diameter at circumference is 90\u00b0 (theorem).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span class=\"katex-eq\" data-katex-display=\"true\">\nangle ACB = 90^\\circ\n<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Reason: Angle in a semicircle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Exam Tip: Always write the reason for each statement, using curriculum-approved language.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Common mistakes:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Not giving a reason for each statement.<\/li>\n\n\n\n<li>Skipping steps or combining too many steps in one line.<\/li>\n\n\n\n<li>Failing to link statements logically using previous results.<\/li>\n<\/ul>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Application<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Proofs are the foundation for solving riders. They help justify why certain properties and relationships hold, which is required in all advanced geometry tasks. Be familiar with common theorems such as the congruent triangles rules, the angle properties of circles and cyclic quadrilaterals, and the midpoint theorem, as these are commonly tested.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Summary<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Success in Euclidean geometry depends on understanding and applying key theorems with clear logical reasoning and correct notation. Use diagrams to visualise problems, show every mathematical step clearly, and always provide full reasons for each step during proofs. Practise with multiple examples and past paper questions to gain confidence and accuracy in problem-solving.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Euclidean Geometry Study Notes Circle geometry Circle geometry focuses on the properties and relationships involving circles, such as chords, tangents, diameters, radii, and angles in circles. Important facts: Example Question: Given a circle with centre O, and chord AB = 6 units. If the perpendicular from O to AB meets AB at point M and [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_breakdance_hide_in_design_set":false,"_breakdance_tags":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-67","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"acf":{"document_name":"Euclidean Geometry","grade":12,"subject":"Mathematics","term":4,"paper":2},"_links":{"self":[{"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/posts\/67","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/comments?post=67"}],"version-history":[{"count":3,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/posts\/67\/revisions"}],"predecessor-version":[{"id":224,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/posts\/67\/revisions\/224"}],"wp:attachment":[{"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/media?parent=67"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/categories?post=67"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/repstaq.com\/study-guide-docs\/wp-json\/wp\/v2\/tags?post=67"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}