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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
Challenge
Challenge: Skipped Counts
Challenge problems (geometry for high schoolers)
Circles
Distance between a point and a line
Geometric constructions
NRICH activities (geometry for high schoolers)
Proving parallelograms with two column proofs
Two column proofs
YouTube videos
1079
Circle Geometry Example Question (worked proof)
Eddie Woo
1232
Parametrics Exam Question (1 of 2: Proving perpendicular lines)
Eddie Woo
1233
Parametrics Exam Question (2 of 2: Circle geometry proof)
Eddie Woo
1293
Formal Geometry Proofs (1 of 3: What does it mean to "prove" something?)
Eddie Woo
1575
Circle Geometry Proof (Touching circles with a second common tangent)
Eddie Woo
1613
Tough Circle Geometry Question (1 of 2: Set up & initial arguments)
Eddie Woo
1614
Tough Circle Geometry Question (2 of 2: Proving points collinear)
Eddie Woo
1629
Congruent Triangles in Circles (1 of 2: Equal chords)
Eddie Woo
1630
Congruent Triangles in Circles (2 of 2: Chord bisector)
Eddie Woo
1645
Tough Circle Geometry Question (2 of 3: Proving a given chord is a diameter)
Eddie Woo
More YouTube videos...
Webpages
59
File:Europe a Prophecy copy K plate 01.jpg
Wikimedia Commons
86
The Pythagorean Theorem: Geometry’s Most Elegant Theorem
MIT BLOSSOMS
110
Geometry
Tarrou's Chalk Talk
Khan Academy videos
1660
Introduction to the Pythagorean theorem
Khan Academy
~
YouTube
1662
Geometric constructions: circle tangent
Khan Academy
~
YouTube
1663
Circles glossary
Khan Academy
~
YouTube
1664
Geometric constructions: perpendicular bisector
Khan Academy
~
YouTube
1665
Finding arc measures with equations
Khan Academy
~
YouTube
1667
Solving for a side in right triangles with trigonometry
Khan Academy
~
YouTube
1670
Inscribed quadrilaterals proof
Khan Academy
~
YouTube
1672
Intro to rotational symmetry
Khan Academy
~
YouTube
1674
Area of inscribed equilateral triangle
Khan Academy
~
YouTube
1676
Trig 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...