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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

    Other resources

    1. Challenge
    2. Challenge: Skipped Counts
    3. Challenge problems (geometry for high schoolers)
    4. Circles
    5. Distance between a point and a line
    6. Geometric constructions
    7. NRICH activities (geometry for high schoolers)
    8. Proving parallelograms with two column proofs
    9. Two column proofs

    YouTube videos

    • 1079Circle Geometry Example Question (worked proof)
      Eddie Woo
    • 1232Parametrics Exam Question (1 of 2: Proving perpendicular lines)
      Eddie Woo
    • 1233Parametrics Exam Question (2 of 2: Circle geometry proof)
      Eddie Woo
    • 1293Formal Geometry Proofs (1 of 3: What does it mean to "prove" something?)
      Eddie Woo
    • 1575Circle Geometry Proof (Touching circles with a second common tangent)
      Eddie Woo
    • 1613Tough Circle Geometry Question (1 of 2: Set up & initial arguments)
      Eddie Woo
    • 1614Tough Circle Geometry Question (2 of 2: Proving points collinear)
      Eddie Woo
    • 1629Congruent Triangles in Circles (1 of 2: Equal chords)
      Eddie Woo
    • 1630Congruent Triangles in Circles (2 of 2: Chord bisector)
      Eddie Woo
    • 1645Tough Circle Geometry Question (2 of 3: Proving a given chord is a diameter)
      Eddie Woo
      • More YouTube videos...

    Webpages

    • 59File:Europe a Prophecy copy K plate 01.jpg
      Wikimedia Commons
    • 86The Pythagorean Theorem: Geometry’s Most Elegant Theorem
      MIT BLOSSOMS
    • 110Geometry
      Tarrou's Chalk Talk

    Khan Academy videos

    • 1660Introduction to the Pythagorean theorem
      Khan Academy ~ YouTube
    • 1662Geometric constructions: circle tangent
      Khan Academy ~ YouTube
    • 1663Circles glossary
      Khan Academy ~ YouTube
    • 1664Geometric constructions: perpendicular bisector
      Khan Academy ~ YouTube
    • 1665Finding arc measures with equations
      Khan Academy ~ YouTube
    • 1667Solving for a side in right triangles with trigonometry
      Khan Academy ~ YouTube
    • 1670Inscribed quadrilaterals proof
      Khan Academy ~ YouTube
    • 1672Intro to rotational symmetry
      Khan Academy ~ YouTube
    • 1674Area of inscribed equilateral triangle
      Khan Academy ~ YouTube
    • 1676Trig challenge problem: trig values & side ratios
      Khan Academy ~ YouTube
      • More Khan Academy videos...

    Khan Academy exercises

    • Solid geometry word problems
      Khan Academy
    • Solve triangles: angle bisector theorem
      Khan Academy
    • Arc measure with equations
      Khan Academy
    • Write standard equation of a circle
      Khan Academy
    • Density word problems
      Khan Academy
    • Coordinate plane word problems: polygons
      Khan Academy
    • Area & perimeter on the coordinate plane
      Khan Academy
    • Inscribed quadrilaterals
      Khan Academy
    • Inscribed shapes
      Khan Academy
    • Features of a circle from its standard equation
      Khan Academy
      • More Khan Academy exercises...