High School Geometry



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Common Core Math Geometry

Geometry Building Blocks

Three Undefined TermsPoint, Line, and Plane Counterexample Writing a Good Definition Postulate, Axiom, Conjecture
Math Converse Line Segments, Rays, Parallel and Skew Lines
Midpoints and Congruent Segments Calculating the Midpoint, Parallel Planes and Lines, Vertex and Diagonals
AnglesTypes and Labeling, Using a Protractor, Angle Bisectors, Supplementary and Complementary Angles
Polygons Types of Triangles, Perimeter, Parts of a Circle
 

Triangles

Triangle Angle Sum
Isosceles Triangles
Triangle Side Inequalities
Triangle Side and Angle Inequalities
Remote Interior Angles

Congruent Triangles

SSS and SAS
ASA and AAS
Hypotenuse Leg (HL)
Why SSA and AAA Don't Work as Congruence Shortcuts

Similar Triangles and Polygons

Solving Proportions
Properties of Similar Polygons
Similarity Shortcuts
Similar Triangles in Circles and Right Triangles
Indirect Measurement

Proportional Segments Between Parallel Lines
Corresponding Parts of Similar Triangles
Angle Bisectors and Opposite Side Ratios
Similarity and Area Ratios
Similarity and Volume Ratios

Diagonals

Number of Diagonals in a Polygon
Number of Handshakes at a Party

Angles and Parallel Lines

Adjacent Angles
Vertical Angles
Corresponding Angles

Alternate Interior Angles
Alternate Exterior Angles
Same Side Interior and Same Side Exterior Angles
Converse of Parallel Lines Theorem

Angles of Polygons

Polygon Angle Sum
Equiangular Polygon Sums
Exterior Angles of a Polygon

Properties of Polygons

Kite Properties
Trapezoid Properties
Triangle Midsegment Properties
Trapezoid Midsegment Properties

Parallelogram Properties
Trapezoid Arch and Panel Design Problem
Rhombus Properties
Rectangle and Square Properties



Area of 2-D Shapes

Area of Parallelograms
Area of Triangles
Area of Trapezoids
Solving Formulas

Area of Kites and Rhombuses
Center and Apothem of Regular Polygons
Area of Regular Polygons

Area of Circles
Area of a Sector
Area of a Segment
Area of an Annulus
Regions Between Circles and Squares

Surface Area of Solids

Surface Area of Prisms
Surface Area of Cylinders
Surface Area of Pyramids

Surface Area of Cone
Surface Area of Sphere
Surface Area of Joined Solids

Volume

3-D Solid Properties
Volume of Prisms
Volume of Cylinders
Volume of Cones

Volume of Pyramids
Solving Equations with Squares and Cubes
Volume of Spheres
Surface Area of Spheres



Transformations

Transformations and Isometries
Translations
Reflections
Rotations
Compositions of Transformations
Glide Reflections

Reflectional Symmetry
Rotational Symmetry
Dilations

Geometry Proofs

CPCTC
Two Column Proofs
Flowchart Proofs
Special Isosceles Triangle Properties

Reasoning

Inductive Reasoning
Deductive Reasoning



Constructions

Duplicating a Line Segment
Duplicating an Angle
Constructing the Perpendicular Bisector
Constructing a Perpendicular at a Point on a Line
Constructing a Perpendicular to a Line

Constructing an Angle Bisector
Constructing Parallel Lines
Constructing Altitudes
Constructing a Median

Constructing a Triangle Midsegment
Point of Concurrency
Circumscribed and Inscribed Circles and Polygons
Constructing the Incenter

Constructing the Circumcenter
Constructing the Orthocenter
Constructing the Centroid

Circles

Locus and Definition of a Circle and Sphere
Central Angles and Intercepted Arcs
Chords and a Circle's Center

Radii to Tangents
Tangent Segments to a Circle
Inscribed Angles
Angles in Semicircles and Chords to Tangents

Cyclic Quadrilaterals and Parallel Lines in Circles
Circumference
Arc Length
Secants

Pythagorean Theorem

Pythagorean Theorem Proofs
Square Root Operations
Using the Pythagorean Theorem to find a Missing Hypotenuse

Using the Pythagorean Theorem to find a Missing Leg
Space Diagonals
Converse of the Pythagorean Theorem

45-45-90 Triangles
30-60-90 Triangles

Distance Formula
Equation of a Circle
Calculating Coordinates in the Unit Circle

Basic Trigonometry

Trigonometric Ratios: Sine
Trigonometric Ratios: Cosine
Trigonometric Ratios: Tangent
Inverse Trigonometric Functions

Angle of Elevation and Depression
Using Sine to Calculate the Area of a Triangle
The Law of Sines
The Law of Cosines


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