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Topic · Grades K to 12

Geometry

Shapes, space, and the reasoning that proves facts about them.

11 subtopics209 lessons
1

Points, lines and planes

25 lessons

The undefined starting objects, and what is built from them.

1.1Points, lines and planes
1.2Angles and how to name themGrade 4
1.3Points, lines, rays and segmentsGrade 4
1.4Angle types and pairs
1.5Parallel linesGrade 4
1.6Acute, right, obtuse and straight anglesGrade 4
1.7Perpendicular linesGrade 4
1.8Midpoints and segment bisectorsMath 8
1.9Distance on a number lineMath 7
1.10Congruent angles, angle addition and bisectorsMath 7
1.11Complementary and supplementary anglesMath 7
1.12Adjacent angles and linear pairsMath 7
1.13Vertical anglesMath 7
1.14Finding unknown angle measuresMath 7
1.15Points, lines and planesGeometry
1.16Lines and planes in spaceGeometry
1.17Alternate and same side anglesMath 8
1.18Corresponding anglesMath 8
1.19Parallel lines and transversals
1.20Perpendicular bisector of a segmentMath 8
1.21Segment length, addition and congruenceMath 8
1.22Segments, rays and length
1.23The parallel postulateGeometry
1.24Distance from a point to a lineGeometry
1.25Locus of pointsGeometry
2

Two-dimensional shapes

26 lessons

Naming and sorting flat shapes by their sides and corners.

2.1Naming circles, triangles, squares and rectanglesKindergarten
2.2Position words: above, below, beside, in front of, behindKindergarten
2.3Two-dimensional shapes
2.4What a circle isMath 6
2.5Composing and decomposing shapesKindergarten
2.6Sides, corners and sorting shapesKindergarten
2.7Building shapes from sticks and clayKindergarten
2.8Defining and non-defining attributes of shapesGrade 1
2.9Polygons
2.10Triangles, quadrilaterals, pentagons and hexagons from their sides and anglesGrade 2
2.11Quadrilaterals
2.12Rhombuses, rectangles and squaresGrade 3
2.13Shapes in more than one category, and quadrilaterals in noneGrade 3
2.14Classifying trianglesGrade 4
2.15Naming and classifying polygonsGrade 4
2.16TessellationsGeometry
2.17Parallelograms, rectangles, rhombuses and squares: what each one guaranteesGrade 5
2.18Regular polygons and their anglesGeometry
2.19Classifying shapes in a hierarchyGrade 5
2.20Trapezoids and kitesGeometry
2.21Angle sums of polygonsGeometry
2.22Properties of a parallelogramGeometry
2.23Rectangles, rhombuses and squaresGeometry
2.24The quadrilateral family treeGeometry
2.25Regular polygons and their circlesGeometry
2.26The apothem of a regular polygonGeometry
3

Solids

26 lessons

Three-dimensional shapes, their surfaces and their insides.

3.1Naming and describing solid shapesKindergarten
3.2Solids
3.3Three-dimensional shapes
3.4Faces, edges and verticesGrade 2
3.5Cylinders and conesMath 6
3.6SpheresMath 8
3.7Prisms and pyramidsMath 6
3.8Nets of solidsMath 6
3.9Volume of prisms and cylindersMath 7
3.10Surface area
3.11PolyhedraMath 6
3.12Cross sections of solidsMath 7
3.13Surface area of prisms and cylindersMath 7
3.14Volume of a cylinderMath 8
3.15Volume of solids
3.16Volume of a sphereMath 8
3.17The five regular solidsGeometry
3.18Surface area of pyramids and conesGeometry
3.19Volume of pyramids and conesMath 8
3.20Composite solids and densityMath 8
3.21Solids of revolutionGeometry
3.22Coordinates and distance in three dimensionsGeometry
3.23Cavalieri's principleGeometry
3.24Surface area of a sphereGeometry
3.25Why the volume formulas hold: dissection, slicing and CavalieriGeometry
3.26Modeling with solids: density and designGeometry
4

Coordinate geometry

14 lessons

Geometry done with numbers on a grid.

4.1Coordinate geometry
4.2Ordered pairs and the first quadrantGrade 5
4.3The coordinate plane
4.4Two number patterns side by side and graphing their pairsGrade 5
4.5Plotting in all four quadrantsMath 6
4.6Points that differ only in sign: reflections across the axesMath 6
4.7Area of a polygon from coordinatesMath 6
4.8Horizontal and vertical distanceMath 6
4.9The distance formulaMath 8
4.10The midpoint formulaGeometry
4.11Classifying figures from coordinatesGeometry
4.12Partitioning a segment in a given ratioGeometry
4.13Perimeter and area from coordinatesGeometry
4.14Coordinate proofs with variablesGeometry
5

Circles

16 lessons

Circumference, area, and the angle and chord theorems inside a circle.

5.1Radius and diameterMath 7
5.2CircumferenceMath 7
5.3Circles
5.4Chords, secants and tangentsGeometry
5.5Area of a circleMath 7
5.6Arcs and central anglesGeometry
5.7Sectors, segments and their areasGeometry
5.8Inscribed polygons and cyclic quadrilateralsGeometry
5.9Tangent propertiesGeometry
5.10Arc lengthGeometry
5.11The inscribed angle theoremGeometry
5.12Angles made by chords, secants and tangentsGeometry
5.13Chord theoremsGeometry
5.14Equation of a circleGeometry
5.15Segment lengths in circlesGeometry
5.16Finding the center and radiusGeometry
6

Triangles

30 lessons

The simplest polygon, and most of geometry's theorems.

6.1Parts of a triangleMath 7
6.2Triangles
6.3Triangle angle sumMath 8
6.4Triangle inequalityMath 7
6.5Drawing triangles from given sides and angles: one, many or noneMath 7
6.6Congruence statements and correspondenceGeometry
6.7Congruent triangles
6.8Isosceles and equilateral trianglesGeometry
6.9The Pythagorean theoremMath 8
6.10Converse of the Pythagorean theoremMath 8
6.11Pythagorean triplesMath 8
6.12Using the Pythagorean theoremMath 8
6.13The Pythagorean theorem in three dimensionsMath 8
6.14Special segments in a triangle
6.15SSS, SAS, ASA, AASGeometry
6.16Triangle centers
6.17Medians and altitudesGeometry
6.18Why AAA and SSA failGeometry
6.19Angle bisectors of a triangleGeometry
6.20Midsegments of triangles and trapezoidsGeometry
6.21Perpendicular bisectors of a triangleGeometry
6.22Sides and angles in orderGeometry
6.23CircumcenterGeometry
6.24Hinge theoremGeometry
6.25IncenterGeometry
6.26Hypotenuse leg congruenceGeometry
6.27Special right trianglesGeometry
6.28Geometric means in a right triangleGeometry
6.29CentroidGeometry
6.30Orthocenter and the Euler lineGeometry
7

Similarity

11 lessons

Same shape, different size.

7.1Similarity
7.2Similar figuresMath 8
7.3Proportions in similar trianglesMath 8
7.4DilationsMath 8
7.5Scale factor and perimeter, area and volumeGeometry
7.6AA similarityMath 8
7.7SSS and SAS similarityGeometry
7.8Triangle proportionality theoremGeometry
7.9Triangle angle bisector theoremGeometry
7.10Similarity transformationsMath 8
7.11What a dilation does to a lineGeometry
8

Transformations

12 lessons

Moving figures: slide, flip, turn, and what stays the same.

8.1Line symmetryGrade 4
8.2Rotational and point symmetryGeometry
8.3Transformations
8.4TranslationsMath 8
8.5ReflectionsMath 8
8.6RotationsMath 8
8.7What rigid motions preserveMath 8
8.8Rigid motions and congruenceMath 8
8.9Composing transformationsMath 8
8.10Rotating about a point other than the originGeometry
8.11Rigid motions defined precisely, and what they preserveGeometry
8.12Two reflections in a rowGeometry
9

Geometric proof

33 lessons

Arguing from definitions and accepted facts to a certain conclusion.

9.1Deductive reasoningGeometry
9.2Inductive reasoningGeometry
9.3Proving the Pythagorean theorem by rearrangementMath 8
9.4Auxiliary linesGeometry
9.5Geometric proof
9.6Given, prove and the diagramGeometry
9.7Converses and biconditional definitionsGeometry
9.8Proofs about parallelograms
9.9Proving a quadrilateral is a parallelogramGeometry
9.10Proving properties of a parallelogramGeometry
9.11Proving properties of an isosceles trapezoidGeometry
9.12Proving the triangle angle sumGeometry
9.13Two-column and paragraph proofsGeometry
9.14Proving a parallelogram is a rectangle or a rhombusGeometry
9.15Proving lines parallelGeometry
9.16Proving parts congruent after the trianglesGeometry
9.17Proving the base angles theoremGeometry
9.18Proving triangles congruent
9.19Proving alternate interior angles congruentGeometry
9.20Proving angle pair theoremsGeometry
9.21Transformational proofGeometry
9.22Properties of equality and congruenceGeometry
9.23Planning a congruence proofGeometry
9.24Proofs about circles
9.25Proving the inscribed angle theoremGeometry
9.26Indirect proofGeometry
9.27Proofs about similar figures
9.28Proving two triangles similarGeometry
9.29Proving a tangent is perpendicular to the radiusGeometry
9.30Proving the Pythagorean theorem with similar trianglesGeometry
9.31Proving the triangle proportionality theoremGeometry
9.32Flowchart proofs and choosing a formatGeometry
9.33Proving the power of a point relationshipsGeometry
10

Compass and straightedge constructions

9 lessons

Copy a segment, bisect an angle, drop a perpendicular, with no ruler markings.

10.1Bisecting a segment and an angleGeometry
10.2Compass and straightedge constructions
10.3Constructing a triangle from given partsGeometry
10.4Copying a segment and an angleGeometry
10.5Perpendicular and parallel lines through a pointGeometry
10.6Why a construction worksGeometry
10.7Constructions with circlesGeometry
10.8Equilateral triangle, square and hexagon in a circleGeometry
10.9Dividing a segment into equal partsGeometry
11

Conic sections

7 lessons

Slice a cone and you get a circle, an ellipse, a parabola, or a hyperbola.

11.1Conic sections from a double conePrecalculus
11.2Focus and directrixPrecalculus
11.3The parabola as a locusPrecalculus
11.4Conic sections
11.5The ellipsePrecalculus
11.6The hyperbolaPrecalculus
11.7Identifying and translating conicsPrecalculus