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▾High school geometry
- ▸Basics of geometry
  - •Proofs in this course
  - •Geometric definitions
  - •Linear pair theorem
  - •Area of a regular polygon
  - •Diagonal length of a right rectangular prism
  - •Distance and midpoint in 3D
  - •Circumcircles and incircles
- ▸Transformations
  - •Preserved properties of rigid transformations
  - •Find measures using rigid transformations
  - •Find the angle of rotation
  - •Find the sequence of rigid transformations
  - •Reflecting figures
  - •Reflecting a point over any non-horizontal line
- ▸Congruence
  - •Congruent polygons
  - •Congruent supplements and complements theorems
  - •ASA and AAS congruence
  - •Isosceles triangle theorem and its converse
  - •SSS congruence
  - •SAS congruence
  - •Converse of the Pythagorean theorem
  - •Proving isosceles trapezoids
- ▸Similarity
  - •Intro to similarity
  - •All circles are similar
  - •Finding angles and side lengths in similar polygons
  - •Finding the scale factor for similar polygons
  - •Third angle theorem
  - •Similar triangles
  - •Ratios of area, surface area, and volume, for similar shapes
  - •Crossed ladders theorem
- ▸Polygons
  - •Perimeter of composite figures
  - •Finding the volume and surface area of composite figures
  - •Sum of the interior angles of a triangle
  - •Sum of interior angles for simple polygons
  - •Sum of exterior angles
  - •Pentagonal tilings
- ▸Incenter and circumcenter of a triangle
  - •Intro to the incenter and circumcenter of a triangle
  - •Perpendicular bisector theorem and its converse
  - •Circumcenter theorem
  - •Angle bisector theorem
  - •Incenter theorem
- ▸Triangles
  - •Euler line
  - •Geometric mean theorems
  - •AM-GM inequality
  - •Triangle angle bisector theorem
  - •Ceva's theorem
  - •Proving the altitude of an isosceles triangle cuts two congruent right triangles
  - •Centroid and orthocenter
  - •Ordering triangle sides and angles
  - •Midsegment and proportionality theorems
  - •Menelaus's theorem
  - •Side splitter theorem
  - •Hinge theorem and its converse
  - •Hypotenuse-leg congruence theorem
  - •Hypotenuse-angle congruence theorem
  - •Areas of triangles and quadrilaterals on grids
  - •Exterior angle theorem
- ▸Quadrilaterals
  - •Diagonals of a kite are perpendicular
  - •Diagonals of a parallelogram bisect each other
  - •Diagonals of a rhombus are perpendicular bisectors
  - •Area of a rhombus from diagonals
  - •Diagonals of a rectangle are congruent
  - •Opposite sides of a parallelogram are congruent
  - •Opposite angles of a parallelogram are congruent
  - •British flag theorem
  - •Cyclic quadrilaterals
  - •Fuhrmann's theorem
  - •Classifying quadrilaterals from four points
- ▸Circle theorems
  - •Thales's theorem and its converse
  - •Central angle theorem
  - •Angles standing on the same arc are congruent
  - •Chord properties
  - •Congruent tangents theorem
  - •Radius and tangent theorem
  - •Radii inside right triangles
  - •Alternate segments theorem
  - •Power of a point
  - •Three squares puzzle
- ▸Volume and surface area
  - •Cavalieri's principle
  - •Volume of prisms and cylinders
  - •Volume and surface area of a sphere
- ▸Analytic geometry
  - •A square within a square

› High school geometry

Transformations

Preserved properties of rigid transformations
Find measures using rigid transformations
Find the angle of rotation
Find the sequence of rigid transformations
Reflecting figures
Reflecting a point over any non-horizontal line