Geometry — Lines, Angles, Polygons, Triangles & Circles - Concept map
Geometry fundamentals including measurement, properties, and relationships of geometric shapes
Related concepts
Lines and Line Segments
Sub concepts
- Points
- Line segments
- Rays
- Parallel lines
- Perpendicular lines
- Intersecting lines
- Transversals
Relationship to central
Basic building blocks that form all geometric shapes
Angles
Sub concepts
- Acute angles
- Right angles
- Obtuse angles
- Straight angles
- Complementary angles
- Supplementary angles
- Vertical angles
- Linear pairs
Relationship to central
Formed by intersection of lines, fundamental to shape properties
Polygons
Sub concepts
- Triangle
- Quadrilateral
- Pentagon
- Hexagon
- Regular polygons
- Irregular polygons
- Convex polygons
- Concave polygons
- Interior angles
- Exterior angles
- Diagonals
Relationship to central
Multi-sided closed figures with specific properties and formulas
Triangles
Sub concepts
- Equilateral
- Isosceles
- Scalene
- Right triangle
- Acute triangle
- Obtuse triangle
- Pythagorean theorem
- Triangle inequality
- Congruent triangles
- Similar triangles
- Special right triangles
Relationship to central
Three-sided polygons with unique properties and classification systems
Circles
Sub concepts
- Radius
- Diameter
- Chord
- Arc
- Sector
- Central angle
- Inscribed angle
- Tangent
- Secant
- Circumference
- Area
Relationship to central
Curved figures with unique properties involving radius, diameter, and arcs
Measurement Formulas
Sub concepts
- Perimeter formulas
- Area formulas
- Surface area formulas
- Volume formulas
- Circumference formula
Relationship to central
Mathematical expressions for calculating perimeter, area, and volume
Concept connections
- Lines and Line SegmentsAnglesIntersecting lines form angles
- AnglesPolygonsPolygons are formed by angles and their sum determines polygon type
- PolygonsTrianglesTriangle is the simplest polygon and building block of other polygons
- Lines and Line SegmentsCirclesTangent and secant lines interact with circles
- AnglesCirclesCentral and inscribed angles are fundamental circle properties
- TrianglesCirclesTriangles can be inscribed in or circumscribed about circles
- Measurement FormulasTrianglesSpecific formulas apply to triangle perimeter, area, and special properties
- Measurement FormulasCirclesUnique formulas for circumference and area of circles
- Measurement FormulasPolygonsDifferent formulas apply based on polygon type and regularity
- Lines and Line SegmentsMeasurement FormulasLine properties determine which measurement formulas to use
Diagrams
Complete Geometry Concept Map
Comprehensive mind map showing all major geometry concepts and their hierarchical relationships
Triangle Classification Decision Tree
Step-by-step decision tree for classifying triangles by sides and angles
Problem-Solving Strategy for Geometry
General problem-solving approach for geometry questions with decision points
Formula Selection Guide
Decision tree for selecting the correct formula based on shape and measurement needed
Common Geometry Question Types in UPCAT
Distribution of geometry question types commonly found in UPCAT examinations