# Geometry

Lesson 1: An investigation into Points, Lines and Planes.

• Define what a point, a line and a plane.
• Define segment, endpoint, ray and Opposite Rays.
• Define What a Postulate is.
• Introduce Postulate 1: through any two points there is exactly one line.
• Postulate 2:Through any three noncollinear points there is exactly one plane containing them.
• Postulate 3: If two points lie in a plane, then the line containing those points lies in the plane.

Lesson 2: Angle Relationships

• Vocabulary: Adjacent Angles, Linear Pair, Complementary Angles, Supplementary Angles and Vertical Angles
• Prove Vertical angles! An easy proof to demonstrate the use of linear pairs as well as an introduction to the transitive property or substitution property.
• Typical Problems and quiz.

Lesson 3: Geometric Reasoning

•  Conditional Statements, converse, inverse and contrapositive.
• There are many real life examples of conditional statements available.
• Logically equivalent statements.
• Quiz: http://www.regentsprep.org/Regents/math/geometry/GP2/PracRC.htm

Lesson 4: Parrallel Lines and Transversals

Lesson 5: Triangles

• Prove Triangle Sum Theorem
• Area of triangles
• Pythagorean Theorem
• Special Right triangles
• Quiz

Lesson 6: Triangle Congruence

• Go over the theorems SSS, SAS, ASA, AAS and HL.

Lesson 7: Introduction to regular Polygons

• Warm Up: Special Right triangles
• Tutor facilitates the creation of the sum of interior angles formula.
• Facilitates the production of the formula  for the measurement of one angle.
• Find the Area of Regular Polygons.

Lesson 8: Circles

• Vocabulary: Arcs, Chords, Tangents, Points of Tangency, Inscribed Angles
• Angle Relationships in Circles
• Segment Relationships in Circles