Geometry

Syllabus

The Basics

  • Line segments and their measures
  • Angles and their measures
  • Classifying angles
  • Angle terminology
  • Angle Addition Postulate
  • Angle relationships
  • Geometric diagrams and notation
  • Parallel Lines and the Coordinate Plane
  • Parallel lines and transversals
  • Proving lines parallel
  • Points on the coordinate plane
  • The Midpoint Formula
  • The Distance Formula
  • Slope and lines
  • Graphing linear equations
  • Writing linear equations

Properties of Triangles

  • Angle bisectors
  • Medians
  • Centroid
  • Triangle Inequality Theorem
  • Inequalities in one triangle

Congruent Triangles

  • Classifying triangles
  • Triangle angle sum
  • Exterior Angle Theorem
  • Triangles and Congruence
  • Proving triangles congruent: SSS and SAS
  • Proving triangles congruent: ASA and AAS
  • Right triangle congruence
  • Isosceles and equilateral triangles

Quadrilaterals and Polygons

  • Classifying quadrilaterals
  • Angles in a quadrilateral
  • Properties of parallelograms
  • Properties of trapezoids
  • Area of triangles
  • Area of quadrilaterals
  • Polygon basics
  • Angles in polygons
  • Area of regular polygons

Similarity

  • Solving proportions
  • Similar polygons
  • Similar triangles
  • Similar right triangles
  • Triangles and parallel lines
  • Proportional parts and parallel lines

Surface Area and Volume

  • Identifying solid figures
  • Volume of prisms and cylinders
  • Nets of prisms and cylinders
  • Surface area of prisms and cylinders
  • Volume of pyramids and cones
  • Nets of pyramids and cones
  • Surface area of pyramids and cones
  • Spheres
  • Similar solids

Right Triangles

  • The Pythagorean Theorem
  • The converse of The Pythagorean Theorem
  • Multi-step Pythagorean Theorem problems
  • Special right triangles
  • Multi-step special right triangle problems

Circles

  • Identifying solid figures
  • Volume of prisms and cylinders
  • Nets of prisms and cylinders
  • Surface area of prisms and cylinders
  • Volume of pyramids and cones
  • Nets of pyramids and cones
  • Surface area of pyramids and cones
  • Spheres
  • Similar solids

Transformations

  • Translations
  • Rotations
  • Reflections

Circles

  • Naming arcs and central angles
  • Measures of arcs and central angles
  • Arcs and chords
  • Circumference and area
  • Inscribed angles
  • Tangents
  • Tangent-tangent angles
  • Secant-tangent angles
  • Segment measures
  • Using equations of circles
  • Writing equations of circles

Trigonometry

  • Finding trig. ratios
  • Finding angle measures
  • Solving for sides of right triangles
  • Multi-step trig. problems
  • Trigonometry and area

Constructions

  • Line segment constructions
  • Perpendicular segment constructions
  • Angle constructions
  • Triangle constructions
  • Medians of a triangle constructions
  • Altitudes of a triangle constructions
  • Angle bisector constructions
  • Circle constructions