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Units of Study

Unit 1:  Basics of Geometry
Points, lines and planes
Measuring and constructing segments
Using midpoint and distance formulas
Perimeter and area in the coordinate plane
Measuring and constructing Angles
Describing pairs of angles

Unit 2: Reasoning and Proofs
Conditional Statements
Inductive and Deductive reasoning
Postulates and Diagrams
Algebraic reasoning
proving statements about segments and angles
Proving geometric relationships

Unit 3: Parallel and Perpendicular
Pairs of lines and angles
Parallel lines and tranversals
Proofs with parallel lines
Proofs with perpendicular lines
Equations of parallel and perpendicular lines

Unit 4 Transformations
Translations
Reflections
Rotations
Congruence transformations
dilations
similarity transformations

Unit 5 Congruent Triangles
Angles of Triangles
congruent polygons
Equilateral and Isosceles triangles
Proving Triangles congruent by SSS, SAS,  ASA, AAS
CTCTC
Coordinate proofs

Unit 6: Relationship with Triangles

Perpendicular bisector theorem and converse

angle bisector theorem and converse

Points of concurrency

Midsegments of a triangle

triangle inequality theorem

triangle longer side/ largest angle

triangle shortest side / smallest angle

Hinge theorem

Unit 7 Quadrilaterals ans Other Polygons

Angles in polygons

Properties of parallelograms

Proving a quadrilateral is a parallelogram

Properties of special parallelogram

rectangles, rhombuses and squares

Properties of trapezoids and kites

Unit 8: Similarity

Similar Polygons

Proving triangles similar

AA

SAS

SSS

Proportionality Theorems

Unit 9:Right Triangles and Trigonometry

The Pythagorean theorem and its converse

Pythagorean inequalities (classifying triangles)

Special Right triangles

Right triangle similarity

Geometric mean

Geometric mean (Altitude/Leg) theorems

Trig ratios

Angle of elevation and depression

Law of Sines

Law of Cosines

Unit 10 Circles

Lines and segments that intersect circles

Finding arc measures

Using chords

Inscribed angles and polygons

Angle relationships in circles

Segment relationships in circles

Circles in the coordinate plane

Unit 11: Circumference, Area and Volume

Circumference and arc length

Areas of circles and sectors

Areas of polygons

3D figures

Volumes of Prisms, cylinders, pyramids, cones and spheres

Surface area of cones and spheres