GEOM ETRY CURRICULUM OUTLINE
I.
Logic
A.
B.
C.
D.
E.
F.
G.
H.
I.
II.
Statement
Negation
Conjunction
Disjunction
Conditional
Biconditional
Converse
Inverse
Contrapositive
a. Logically equivalent
Transformation Geometry
A. Symmetry
1. Line
2. Rotational
3. Point
B. Reflections
C. Translations
D. Rotations
E. Dilations
F. Compositions
III. Geometry
A. Undefined terms, definition
B. Triangles
1. Types by sides and by angles
2. Median
3. Altitude
4. Angle bisector
5. Perpendicular bisector
6. Sum of the interior angles
7. Exterior angle
8. Isosceles triangles
9. Triangle inequalities
10. Larger side – larger angle
IV. Parallel lines
A. Vertical angles
B. Alternate interior angles
C. Alternate exterior angles
D. Corresponding angles
E. Same side interior angles
F. Same side exterior angles
G. Complementary and supplementary angles
V. Right Triangles
A. Pythagorean theorem
B. Special right triangles
1. 30-60-90
2. 45-45-90
C. Mean proportional
D. Similar triangles
E. Proportions
F. Segment joining the midpoints of the sides
VI. Polygons
A. Regular polygons
B. Sum of the interior angles of a polygon
C. Sum of the exterior angles of a polygon
D. Number of sides of a regular polygon
E. Find exterior and interior angles of a regular polygon
VII. Special quadrilaterals
A. Parallelograms
B. Rectangles
C. Rhombuses
D. Squares
E. Trapezoids
1. Isosceles trapezoids
VIII. Circles
A. Terms and definitions
B. Central angle
C. Inscribed angle
D. Angle formed by chord and tangent
E. Angle formed by 2 tangents
F. Angle formed by 2 secants
G. Angle formed by a tangent and a secant
H. Lengths
1. 2 chords
2. 2 tangents
3. 2 secants
4. Tangent and secant
I. Common tangents
IX. Three dimensions
A. Parallel and perpendicular lines and planes
B. Polyhedrons
C. Rectangular Solids
D. Pyramids
E. Cylinders
F. Cones
G. Spheres
X. Coordinate Geometry
A. Midpoint
B. Distance
C. Slope – Formula
1. Parallel lines
2. Perpendicular lines
D. Equation of a line
1. Point-Slope form
2. Slope-Intercept form
3. Equation of lines that are parallel and perpendicular to a given line
E. Area of triangles and quadrilaterals
F. Proofs
XI. Euclidean Proofs-Part 1
A. Segment Addition
B. Angle Addition
C. Supplement Axiom
D. Complement Axiom
E. Isosceles triangle theorems
F. Parallel lines theorems and converses
XII. Congruent triangles
1. SSS
2. SAS
3. ASA
4. AAS
5. CPCTC
XIII. Indirect Proofs
XIV. Quadrilaterals
A. Proving quads are parallelograms
B. Rectangles
C. Rhombuses
D. Squares
E. Trapezoids
XV. Similar triangles
A. AA
B. Proportions (Definition of ~triangles)
XVI. Locus
A.
B.
C.
D.
E.
F.
G.
H.
Equidistant from a point
Equidistant from a line
Equidistant from sides of an angle
Equidistant from 2 points
Equidistant from 2 parallel lines
Equidistant from 2 intersecting lines
Equation of a circle
Compound loci
XVII.
Constructions
A. Bisect a segment
B. Construct a segment = to a given segment
C. Bisect an angle
D. Construct an angle = to a given angle
E. Construct a line perpendicular to a given line through a given pt on the line
F. Construct a line perpendicular to a given line through a given pt outside the line
G. Construct the median to a given side of a given triangle
H. Construct the altitude to a given side of a given triangle
I. Construct a line parallel to a given line through a given pt
J. Construct a 60 angle
K. Construct a triangle ~ to a given triangle
L. Construct a triangle given 3 segments
M. Construct an equilateral triangle
XVIII.
Graphing Quadratic –linear equations