Course Building Blocks

1
Course Building Blocks Key Concepts

• 10. Circles
• Use of Arcs, Angles,
• Segments to Solve Real
• Life Problems
• Use Graphs to Model
• Real Life Situations

A P P L I CATION
A P P L I CATION
12. Surface Area Volume

• 11. Area of
• Polygons Circles
• Angles Measures
• Area of Polygons
• Comparing Perimeter
• Area of Similar Figures
• Circumference
• Area of Circles

• Calculating
• SA Volume for
• Various Solids
• Using SA
• Volume in Real
• Life Situations

• 9. Right Triangles
• Trigonometry
• - Properties of Right Triangles
• General, Special, Similar
• Application of Right Triangles
• Trig - Triangle Measures Vectors

• Similarity
• - 4 Ways to Prove Triangles are Similar
• - Using Similar Polygons to Solve Real Life
  Problems

• 7. Transformations
• 3 Ways to describe Motion of Geometric
  Figures
• Transformation in real life
• Reflection, Rotation, Translation

F O U N D A T I O N
F O U N D A T I O N

• Properties of Triangles
• - Properties of Special Lines Segments related
  to Triangles
• - Compare Side Length Angle Measurement in
  Triangles

4. Congruent Triangles - Proving Triangles are
Congruent - Using Congruent Triangles to
Solve Real
Life Problems

• Quadrilaterals
• - Classifying Using Special Qs
• - Writing Proofs
• - Area of Triangles Quads

2. Reasoning Proofs - Conditional
Statements - If-Then Logic - Converse /
Inverse - 2 Column / Paragraph Proofs

• Perpendicular Parallel
• Lines
• - Properties
• - Six Methods to Prove Parallel
• - Writing Linear Equations

• Basics of Geometry
• - Measure / Segment Angles
• - Bisecting Segments Angles
• - Relationships Special Pairs

2
Chapter 2 Reasoning and Proofs

• The Bigger Picture
• - Formal Geometry consists of undefined terms,
  defined terms, postulates, and theorems.
• The Goal for writing a proof is to convince
  someone about the truth of a statement.
• Structure and Logic are essential in building a
  solid argument and proof in geometry, and real
  life

The What and the Why

• Use the Laws of Logic to Write a Logical
• Argument
• Write true statements about various scenarios
• using a list of facts regarding the topic
• Use properties of Algebra
• Use and incorporate properties from Algebra to
• support and further define logic
• Use Properties of Length and Measure
• Find the measure of an angle to apply it to a
  real life
• scenario such as a banked turn in constructing a
  highway
• Use Properties of Segment Congruence to
• Prove Statements about other Segments
• Prove statements about segments in real life
  objects such
• as in bridge construction
• Use the Properties of Angle Congruence to Prove
• Properties about Special Pairs of Angles
• Decide which angles are congruent when
  constructing
• symmetrical and a-symmetrical objects

• Recognize and Analyze Conditional
• Statements
• Write Inverse, converse, and
• Contra-positive Statements
• -Use postulates about points, lines and planes
• to analyze real life scenarios by reversing the
  logic
• Recognize and Use definitions and
• Bi-Conditional Statements to structure
• Logical Proofs
• Rewrite postulates in a form that is necessary
  for
• solving a problem
• Use for analyzing geographic relationships
• Use Symbolic Notation to Represent
• Logical Statements
• Assist in deciding if a logical statement is
  actually
• Valid

3
Lesson Opener Conditional Statements
Venn Diagram
Animals
Dogs
Beagles
Hartford
4
Conditional Statements

• Conditional Statement If, then format.
• Converse Flipping the Logic
• Still if, then format, but we switch the
  hypothesis and conclusion
• Negation We can alter a statement by converting
  it to its negative form.
• Inverse Negating the hypothesis and conclusion
  of the original conditional statement
• Contra-positive Negating the hypothesis and
  conclusion of the of the Converse
• Equivalent Statements When two statements are
  both true or both false.
• A Conditional statement is equivalent to its
  contra-positive
• Similarly, an inverse and converse of any
  conditional statement will be equivalent.