Concept Enumerations
That is a perfect course description. Now for our next step, use this course description to create an enumerated list of the 150 core concepts taught in this course. Return this list as a numbered list with only a short concept label in each list element. Use short names and abbreviations when possible.
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- Point
- Line
- Plane
- Angle
- Segment
- Ray
- Collinear points
- Coplanar points
- Intersection
- Parallel lines
- Perpendicular lines
- Midpoint
- Bisector
- Angle bisector
- Perp bisector
- Acute angle
- Right angle
- Obtuse angle
- Straight angle
- Reflex angle
- Adjacent angles
- Vertical angles
- Complementary angles
- Supplementary angles
- Linear pair
- Transversal
- Corresponding angles
- Alt int angles
- Alt ext angles
- Same-side int angles
- Same-side ext angles
- Triangle
- Scalene triangle
- Isosceles triangle
- Equilateral triangle
- Acute triangle
- Right triangle
- Obtuse triangle
- Triangle sum theorem
- Ext angle theorem
- Congruent triangles
- SSS congruence
- SAS congruence
- ASA congruence
- AAS congruence
- HL congruence
- Triangle inequality
- Similar triangles
- AA similarity
- SSS similarity
- SAS similarity
- Proportional sides
- Pythagorean theorem
- 45-45-90 triangle
- 30-60-90 triangle
- Quadrilateral
- Parallelogram
- Rectangle
- Square
- Rhombus
- Trapezoid
- Isosceles trapezoid
- Kite
- Properties of parallelogram
- Properties of rectangle
- Properties of rhombus
- Properties of square
- Properties of trapezoid
- Midsegment theorem
- Polygon interior angles
- Polygon exterior angles
- Circle
- Radius
- Diameter
- Chord
- Tangent
- Secant
- Arc
- Central angle
- Inscribed angle
- Arc length
- Sector area
- Circumference
- Equation of circle
- Distance formula
- Midpoint formula
- Slope
- Slope-intercept form
- Point-slope form
- Standard form (line)
- Parallel lines (coord)
- Perpendicular lines (coord)
- Reflection
- Rotation
- Translation
- Dilation
- Transformation
- Rigid motion
- Isometry
- Symmetry
- Line symmetry
- Rotational symmetry
- Tessellation
- Glide reflection
- Composite transformations
- Preimage
- Image
- Vector
- Directed line segment
- Component form
- Solid geometry
- Prism
- Cylinder
- Pyramid
- Cone
- Sphere
- Surface area (SA)
- Volume (Vol)
- SA of prism
- SA of cylinder
- SA of pyramid
- SA of cone
- SA of sphere
- Vol of prism
- Vol of cylinder
- Vol of pyramid
- Vol of cone
- Vol of sphere
- Nets
- Cross section
- Euler's formula
- Congruent figures
- Similar figures
- Scale factor
- Inductive reasoning
- Deductive reasoning
- Conditional statement
- Converse
- Inverse
- Contrapositive
- Biconditional
- Proof
- Two-column proof
- Paragraph proof
- Flowchart proof
- Coordinate proof
- Geometric constructions
- Compass and straightedge
- Constructing bisectors
- Constructing parallels
Workflow
Breaking down concepts
I'm listing 150 core geometry concepts for a high-school course, using short names and abbreviations. The list is numbered, each concept clearly labeled.
Unveiling core concepts
I'm detailing fundamental geometry concepts, including points, lines, triangles, polygons, circles, coordinate geometry, transformations, and solid geometry. Each topic will be expanded to identify at least 150 individual concepts.
Identifying geometric terms
I'm working through various geometric concepts such as angles, triangles, and congruence through the exploration of terms like acute, obtuse, right, and straight angles, as well as different types of triangles and their properties.
Examining geometric shapes
I'm mapping out the study of various geometric forms, ranging from triangles like 45-45-90 and 30-60-90, to quadrilaterals such as parallelograms, rectangles, and trapezoids, each with their unique properties.
Breaking down math insights
I'm outlining a comprehensive list of 150 concepts in geometry, including various solids and their properties, geometric constructions, logical reasoning, proof types, and specific triangle properties.