---
type: CKG Bundle
title: Geometry
tags: [STEM & Engineering]
timestamp: 2026-06-18T00:00:00Z
ckg:
  id: geometry-course
  nodes: 200
  license: CC BY 4.0
  source: Graphify.md ckg-mcp
---

# Geometry — Compressed Knowledge Graph

```csv
1,Point,,FOUND
2,Line,1,FOUND
3,Plane,1,FOUND
4,Ray,1|2,FOUND
5,Line Segment,1|2,FOUND
6,Angle,4|5,FOUND
7,Vertex,1|6,FOUND
8,Collinear Points,1|2,FOUND
9,Coplanar Points,1|3,FOUND
10,Intersection,2|3,FOUND
11,Parallel Lines,2,LINES
12,Perpendicular Lines,2|6,LINES
13,Skew Lines,2|3,LINES
14,Inductive Reasoning,,LOGIC
15,Deductive Reasoning,14,LOGIC
16,Conjecture,14,LOGIC
17,Counterexample,16,LOGIC
18,Conditional Statement,15,LOGIC
19,Hypothesis,18,LOGIC
20,Conclusion,18,LOGIC
21,Converse,18,LOGIC
22,Inverse,18,LOGIC
23,Contrapositive,18|21,LOGIC
24,Biconditional Statement,18|21,LOGIC
25,Postulate,15,LOGIC
26,Theorem,25,LOGIC
27,Proof,15|26,LOGIC
28,Two-Column Proof,27,LOGIC
29,Paragraph Proof,27,LOGIC
30,Flow Chart Proof,27,LOGIC
31,Indirect Proof,27|17,LOGIC
32,Acute Angle,6,ANGLE
33,Right Angle,6,ANGLE
34,Obtuse Angle,6,ANGLE
35,Straight Angle,6,ANGLE
36,Complementary Angles,6|32|33,ANGLE
37,Supplementary Angles,6|35,ANGLE
38,Adjacent Angles,6,ANGLE
39,Vertical Angles,6|10,ANGLE
40,Linear Pair,6|38,ANGLE
41,Angle Bisector,6|5,ANGLE
42,Midpoint,5,FOUND
43,Segment Bisector,5|42,FOUND
44,Perpendicular Bisector,12|43,LINES
45,Distance Formula,5,LINES
46,Midpoint Formula,42,LINES
47,Compass Construction,,CONST
48,Straightedge Construction,,CONST
49,Copying a Segment,47|48|5,CONST
50,Copying an Angle,47|48|6,CONST
51,Bisecting a Segment,47|48|42,CONST
52,Bisecting an Angle,47|48|41,CONST
53,Constructing Perpendiculars,47|48|12,CONST
54,Constructing Parallels,47|48|11,CONST
55,Translation,,TRANS
56,Rotation,,TRANS
57,Reflection,,TRANS
58,Dilation,,TRANS
59,Rigid Motion,55|56|57,TRANS
60,Image,55,TRANS
61,Pre-Image,55,TRANS
62,Composition of Transformations,55|56|57,TRANS
63,Congruent Figures,59,TRANS
64,Corresponding Parts,63,TRANS
65,Triangle Congruence,63|84,TRI
66,SSS Congruence,65|5,TRI
67,SAS Congruence,65|5|6,TRI
68,ASA Congruence,65|6,TRI
69,AAS Congruence,65|6,TRI
70,HL Congruence,65|89,TRI
71,CPCTC,65|64,TRI
72,Transversal,2|11,LINES
73,Corresponding Angles,72|6,ANGLE
74,Alternate Interior Angles,72|6,ANGLE
75,Alternate Exterior Angles,72|6,ANGLE
76,Same-Side Interior Angles,72|6,ANGLE
77,Parallel Postulate,11|25,LINES
78,Slope,2,LINES
79,Slope-Intercept Form,78|2,LINES
80,Point-Slope Form,78|1,LINES
81,Equations of Parallel Lines,11|79,LINES
82,Equations of Perpendicular Lines,12|78,LINES
83,Coordinate Proof,27|78,LOGIC
84,Triangle,1|2|6,TRI
85,Scalene Triangle,84|5,TRI
86,Isosceles Triangle,84|5,TRI
87,Equilateral Triangle,84|5,TRI
88,Acute Triangle,84|32,TRI
89,Right Triangle,84|33,TRI
90,Obtuse Triangle,84|34,TRI
91,Triangle Sum Theorem,84|26,TRI
92,Exterior Angle Theorem,84|26,TRI
93,Third Angle Theorem,91,TRI
94,Base Angles Theorem,86|26,TRI
95,Triangle Inequality Theorem,84|26,TRI
96,Hinge Theorem,84|26,TRI
97,Median of a Triangle,84|42,TRI
98,Altitude of a Triangle,84|12,TRI
99,Perpendicular Bisector Triangle,84|44,TRI
100,Angle Bisector of Triangle,84|41,TRI
101,Centroid,97,TRI
102,Orthocenter,98,TRI
103,Circumcenter,99,TRI
104,Incenter,100,TRI
105,Polygon,1|2,POLY
106,Regular Polygon,105,POLY
107,Interior Angles of Polygon,105|6,POLY
108,Exterior Angles of Polygon,105|6,POLY
109,Quadrilateral,105,POLY
110,Parallelogram,109|11,POLY
111,Rectangle,110|33,POLY
112,Rhombus,110|5,POLY
113,Square,111|112,POLY
114,Trapezoid,109|11,POLY
115,Isosceles Trapezoid,114|86,POLY
116,Kite,109,POLY
117,Pentagon,105,POLY
118,Hexagon,105,POLY
119,Octagon,105,POLY
120,Tessellation,106,POLY
121,Similar Figures,58,SIM
122,Scale Factor,58|121,SIM
123,Similarity Ratio,121|122,SIM
124,AA Similarity,121|6,SIM
125,SAS Similarity,121|5|6,SIM
126,SSS Similarity,121|5,SIM
127,Proportional Segments,121|5,SIM
128,Geometric Mean,121,SIM
129,Altitude to Hypotenuse,89|98|128,SIM
130,Pythagorean Theorem,89|26,SIM
131,Pythagorean Triple,130,SIM
132,Converse Pythagorean Theorem,130|21,SIM
133,Distance in Coordinate Plane,45|130,SIM
134,Sine Ratio,89,SIM
135,Cosine Ratio,89,SIM
136,Tangent Ratio,89,SIM
137,Inverse Trigonometric Functions,134|135|136,SIM
138,Angle of Elevation,6|134,SIM
139,Angle of Depression,6|134,SIM
140,Indirect Measurement,121|134,SIM
141,Circle,1,CIRC
142,Center of Circle,141|1,CIRC
143,Radius,141|5,CIRC
144,Diameter,141|5|143,CIRC
145,Chord,141|5,CIRC
146,Secant,141|2,CIRC
147,Tangent to Circle,141|2|12,CIRC
148,Point of Tangency,147|1,CIRC
149,Central Angle,141|6,CIRC
150,Inscribed Angle,141|6,CIRC
151,Intercepted Arc,149|150,CIRC
152,Major Arc,141|151,CIRC
153,Minor Arc,141|151,CIRC
154,Semicircle,141|144,CIRC
155,Arc Length,141|151,CIRC
156,Sector,141|149,CIRC
157,Segment of Circle,141|145,CIRC
158,Inscribed Polygon,141|105,CIRC
159,Circumscribed Polygon,141|105|147,CIRC
160,Equation of Circle,141|78,CIRC
161,Area of Rectangle,111,AREA
162,Area of Square,113,AREA
163,Area of Parallelogram,110,AREA
164,Area of Triangle,84,AREA
165,Area of Trapezoid,114,AREA
166,Area of Rhombus,112,AREA
167,Area of Kite,116,AREA
168,Area of Regular Polygon,106,AREA
169,Area of Circle,141,AREA
170,Circumference,141,AREA
171,Pi,141|143,AREA
172,Perimeter,105,AREA
173,Prism,105|3,AREA
174,Pyramid,105|84,AREA
175,Cylinder,141|173,AREA
176,Cone,141|174,AREA
177,Sphere,141,AREA
178,Polyhedron,105|3,AREA
179,Face,178|105,AREA
180,Edge,178|5,AREA
181,Lateral Face,173|179,AREA
182,Lateral Edge,173|180,AREA
183,Base of Solid,173,AREA
184,Height of Solid,173|12,AREA
185,Surface Area,173,AREA
186,Lateral Surface Area,185|181,AREA
187,Volume of Prism,173|161,AREA
188,Volume of Pyramid,174|164,AREA
189,Volume of Cylinder,175|169,AREA
190,Volume of Cone,176|169,AREA
191,Volume of Sphere,177|169,AREA
192,Cross-Section,173|3,AREA
193,Cavalieri's Principle,192|185,AREA
194,Net of Solid,178|179,AREA
195,Scale Drawing,121|122,APP
196,Scale Model,121|122,APP
197,Optimization Problem,185|187,APP
198,Modeling with Geometry,121|195,APP
199,Design Challenge,198|197,APP
200,Geometric Proof Portfolio,27|28|29|30,APP
```