Core Math: Geometry

Table of Contents

UNIT 1: LINES AND ANGLES

Lesson 1.1 - Lines

  • Points and lines
  • Rays and line segments
  • Shapes made from points, lines, surfaces, and solids

Lesson 1.2 - Measuring Angles

  • Angles
  • How to measure angles
  • Angle rotation and degrees
  • Angle quarter turn; angle half turn; angle full turn
  • Angle vertex
  • Angle symbols
  • Size of angles

Lesson 1.3 - Types of Angles

  • Types of angles
  • Straight and right angles
  • Acute and obtuse angles
  • Reflex angles
  • Supplementary angles
  • Complementary angles

UNIT 2: INTERSECTIONS AND PARALLELS

Lesson 2.1 - Intersecting Lines

  • Intersecting lines and opposite angles
  • The Opposite Angle Theorem
  • Perpendicular lines
  • Mathematical theorems and proof of a theorem

Lesson 2.2 - Equal Angles

  • Parallel lines
  • Transversals
  • Parallel lines and alternate angles
  • The Alternate Angle Theorem
  • Parallel lines and corresponding angles
  • The Corresponding Angle Theorem

Lesson 2.3 - Supplementary Angles

  • Parallel lines and supplementary angles
  • Parallel lines and interior angles
  • The Interior Angle Theorem

Lesson 2.4 - Angle Problem Solving

  • Solving for missing angles with intersecting lines
  • Solving for missing angles with parallel lines and transversals
  • Applying angle theorems to solve for missing angles

UNIT 3: TRIANGLES

Lesson 3.1 - Triangles

  • The properties of triangles
  • Vertices and interior angles in triangles
  • Acute triangles
  • Right triangles
  • Obtuse triangles
  • Use of a compass to draw arcs

Lesson 3.2 - Special Triangles

  • Equilateral triangles
  • Isosceles triangles
  • Scalene triangles
  • Size of interior angles vs. side of length
  • The Isosceles Triangle Theorem

Lesson 3.3 - Triangle Angle Sum Theorem

  • Proof of the Triangle Angle Sum Theorem
  • Interior angles of triangles

Lesson 3.4 - Exterior Angle Sum Theorem

  • Exterior Angle Sum Theorem
  • Proof of Exterior Angle Sum Theorem

Lesson 3.5 - Triangle Problem Solving

  • Learn how to solve for missing angles using
  • Triangle theorems and angle facts

Lesson 3.6 - Pythagorean Theorem

  • The hypotenuse of a right triangle
  • The Pythagorean Theorem

UNIT 4: PLANE SHAPES

Lesson 4.1 - Quadrilaterals

  • Plane shapes
  • Squares, rhombi, parallelograms, and trapezoids

Lesson 4.2 - Polygons

  • Names of common polygons
  • Properties of polygons
  • Polygons, pentagons, hexagons, heptagons, octagons, nonagons, and decagons

Lesson 4.3 - Regular Polygons

  • Properties of regular polygons

Lesson 4.4 - Circles

  • The parts of a circle
  • Using a compass to draw a circle or draw arcs

Lesson 4.5 - Ellipses

  • Parts of an ellipse
  • Elliptical shapes
  • Lines of symmetry in ellipses

UNIT 5: CONSTRUCTIONS

Lesson 5.1 - Angle Bisectors

  • Construct an angle bisector

Lesson 5.2 - Perpendiculars from a Line

  • Construct a perpendicular from a line

Lesson 5.3 - Perpendiculars to a Line

  • Construct a perpendicular to a line

Lesson 5.4 - Right Bisectors

  • Construct right bisectors

Lesson 5.5 - The Circumcircle

  • Circumcircles
  • Find a circumcenter
  • Construction of a circumcircle

Lesson 5.6 - The Incircle

  • Incircles
  • Incircle and inradius
  • Construction of an incircle

Lesson 5.7 - Parallel Lines

  • Construction of parallel lines
  • Using a compass

UNIT 6: TRANSFORMATION OF SHAPES

Lesson 6.1 - Congruency

  • The properties of congruent shapes

Lesson 6.2 - Translations

  • Translations of shapes
  • Pre-image and translated image

Lesson 6.3 - Reflections

  • Properties of reflected shapes
  • Mirror and reflected image
  • Pre-image and reflected image

Lesson 6.4 - Rotations

  • Rotation of shapes
  • Pre-image and rotated image
  • Center of rotation

Lesson 6.5 - Magnifications

  • Magnification and dilation of shapes
  • Magnification factor; scaling shapes; image; pre-image

UNIT 7: USES OF TRANSFORMATIONS

Lesson 7.1 - Similarity

  • The properties of similar shapes

Lesson 7.2 - Reflective Symmetry

  • Reflective symmetry
  • Axis of symmetry and reflected shapes

Lesson 7.3 - Rotational Symmetry

  • Rotational symmetry
  • Center of rotational symmetry

Lesson 7.4 - Tessellations I

  • The tessellation or tiling of shapes
  • The properties of tessellated or tiled shapes
  • Interior angles of tessellated polygons

Lesson 7.5 - Tessellations Ii

  • The tessellation of parallelograms and distorted parallelograms
  • Tessellated polygons

UNIT 8: SOLID SHAPES

Lesson 8.1 - Cubes, Prisms, Pyramids

  • Polyhedra
  • The properties of cube shapes
  • The properties of prism shapes
  • The properties of pyramid shapes

Lesson 8.2 - Cylinders, Cones, Spheres

  • The properties of cylinder shapes
  • The properties of cone shapes
  • The construction of sphere shapes

Lesson 8.3 - Constructing Solid Shapes

  • The construction of solid shapes
  • Nets of solid shapes
  • Three dimensional shapes

APPENDICIES

  • Appendix A - Glossary
  • Appendix B - Geometry Facts and Theorems