Geometry Notes – 1.1 Patterns and Inductive Reasoning

Inductive Reasoning:

Examples:

Conjecture:

Counterexample:

Examples:

Geometry Notes – 1.3 Points, Lines and Planes

Point:

Space:

Line:

Collinear:

Plane:

Coplanar:

Postulate:

1-1

1-2

1-3

1-4

Geometry Notes – 1.4 Segments, Rays, Parallel Lines and Planes

Segment:

Ray:

Opposite Rays:

Parallel Lines:

Skew Lines:

Parallel Planes:

Geometry Notes – 1.5 Measuring Segments

Postulate 1-5:

What’s absolute value???

Congruent segments:

Postulate 1-6:

Example with solving:

Geometry Notes – 1.6 Measuring Angles

Angle:

Types of angles:

Congruent angles:

Identifying Pairs of Angles:

Example:

Geometry Notes – 1.7 Basic Constructions

Construction:

Constructing Congruent Angles:

Perpendicular Bisector:

Angle Bisector:

Geometry Notes – 1.8 The Coordinate Plane

Quadrants:

The Distance Formula:

Example:

The Midpoint Formula:

Example:

Geometry Notes – 1.9 Perimeter, Circumference and Area

Summary:

Examples:

If perimeter is equal, will area also be equal???

Geometry Notes – 2.1 Conditional Statements

Conditional:

Hypothesis:

Conclusion:

Examples:

Truth Value of a conditional:

Converse:

Example:

If the conditional is true is the converse true???

Symbols for conditionals:Geometry Notes – 2.2 Biconditionals and Definitions

Biconditional:

Example:

Symbolic Form:

Definitions:

Examples (good or bad):

Geometry Notes – 2.3 Deductive Reasoning

Deductive logic:

Property: Law of Detachment

Example:

Property: Law of Syllogism

Example:

Geometry Notes – 2.4 Reasoning in Algebra

Using equation solving in Geometry

2y 3y-9 AC = 21

A B C

Properties of Congruence:

Reflexive:

Symmetric:

Transitive:Geometry Notes – 2-5 Proving Angles Congruent

2x + 10

x Total angle = 139

2x + 404x

Middle ray bisects large angle

Vertical Angles:

Algebraic Example:

Supplementary:

Complementary:

Examples:

Can two angles be congruent and supplementary????

Geometry Notes – 3.1 Properties of Parallel Lines

Corresponding Angles:

Interior/Exterior Angles:

Same Side Interior/Exterior Angles:

Alternate Interior and Exterior Angles:

Two Column Proof Example:

Geometry Notes – 3.2 Proving Lines Parallel

Postulate 3-2:

Two Column Proof of parallel lines:

Examples of parallel with Algebra:

Geometry Notes – 3.3 Parallel and Perpendicular Lines

a

b

1

2

4

Theorem 3-9:

Theorem 3-10

Theorem 3-11

Geometry Notes – 3.4 Triangle Sum Theorem

Triangle Sum Theorem:

Example:

Triangle Classifications:

Triangle Exterior Angle Theorem:

Example:

Geometry Notes – 3.5 Polygon Angle Sum Theorem

Polygon Angle Sum Theorem:

Examples:

Geometry Notes – 3.6 & 3.7 Slope and Parallel/Perpendicular Lines

Slope Formula:

Example:

Slope-Intercept Form:

Example:

Standard Form:

Example:

Parallel Lines (slope):

Perpendicular Lines (slope):

Geometry Notes – 3.8 Constructing Parallel and Perpendicular

Parallel:

Perpendicular:

Geometry Notes – Coordinate Unit (1.8) Distance & Midpoint

Quadrants:

The Distance Formula:

Example:

The Midpoint Formula:

Example:

Geometry Notes – Coordinate Unit (12.5) Equation for Circles

Equation for a Circle : where (h,k) is the center and r is radius. This should look like Pythagorean Theorem again.

Geometry Notes – Coordinate Unit 3-Dimensional Coordinates

Example Plotting using the Giant Graph: (over, over, up)

Practice plotting:

Three Dimension Distance Formula:

Example:

Geometry Notes – 5.1 Midsegments of Triangles

Midsegment:

Picture:

Midsegment Theorem:

Examples:

Geometry Notes – 5.2 Bisectors of Triangles

What does a bisector mean???

What would this look like?

Applying this to angle bisectors:

Examples:

Geometry Notes – 5.3 Concurrent Lines, Medians, Altitudes

Concurrent:

Point of Concurrency:

Circumcenter of a Triangle:

Example with coordinates:

Incenter of a triangle:

Medians in a triangle (centroid):

Altitudes of a triangle (orthocenter):

Geometry Notes – 5.4 Inverses, Contrapositives, Indirect Reasoning

Inverse:

Example:

Contrapositive:

Examples:

What is indirect reasoning?

Contradicting statements:

Geometry Notes – 5.5 Inequalities in Triangles

Connections between angles and sides (sizes):

Examples:

Triangles Inequality:

Examples:

Geometry Notes – 6.1 Classifying Quadrilaterals

Name Definition Sketch

Quadrilateral Hierarchy:

Geometry Notes – 6.2 Properties of Parallelograms

What do you know about opposite sides???

Consecutive Angles???

Opposite Angles:

Diagonals of parallelograms:

Proving that a quadrilateral is a parallelogram:

Geometry Notes – 6.4 Special Parallelograms

Diagonals in a rhombus:

Diagonals in a rectangle:

Examples:

Geometry Notes – 6.5 Trapezoids and Kites

Parts of a Trapezoid:

Properties:

Parts of Kites:

Properties:

Geometry Notes – 6.6 Placing Figures in the Coordinate Plane

Think about letter coordinates and their relationships instead of number coordinates.

Must know properties of your shapes to do this!!!

Examples:

Geometry Notes – 7.1 Ratios and Proportions

Ratio:

Proportion:

Cross Products:

Examples:

Ratio using sides:

Geometry Notes – 7.2 Similar Polygons

Similar:

Similarity Ratio:

Examples:

Geometry Notes – 7.3 Proving Triangles Similar

Angle-Angle Similarity:

Examples:

Side-Angle-Side Similarity:

Examples:

Side-Side-Side Similarity:

Examples:

Geometry Notes – 7.5 Proportions in Triangles

Side-Splitter Theorem:

Picture:

Angle-Bisector Proportions Theorem:

Picture:

Examples:

Geometry Notes – 4.1 Congruent Figures

Congruent Polygons:

Position Changes:

Third Angle Theorem:

Example:

Does this guarantee triangles congruent?

Two column proof with picture:

Geometry Notes – 4.2/4.3 Triangle Congruences SSS,SAS,ASA,AAS

Importance:

SSS:

Drawing:

SAS:

Drawing:

ASA:

Drawing:

AAS:

Drawing:

Examples:

Geometry Notes – 4.4 CPCTC

CPCTC –

Two-Column Proof Examples:

Geometry Notes – 4.5 Isosceles and Equilateral Triangles

Isosceles Triangle Parts and Theorems:

Equilateral Theorems:

Examples:

Geometry Notes – 4.6 HL Congruence

Right Triangle:

HL Congruence (hypotenuse-leg):

Proof Example:

Geometry Notes – 4.7 Using CPCTC

Overlapping Triangles:

Common sides and angles:

Proof with overlapping triangles:

Geometry Notes - 8.1 Pythagorean Theorem and its Converse

A little History Blurb:

The Theorem:

The Proof:

The Converse:

Example 1:

Example 2:

Pythagorean Triples:

Geometry Notes – 8.2 Special Right Triangles

45-45-90:

30-60-90 Triangles

Examples:

Geometry Notes – 8.3/8.4 Trigonometry of a Right Triangle

Parts of a right triangle

Parts of a right triangle

SIN:

COS:

TAN:

Matching Sides:

Mnemonic Device:

Examples:

Geometry Notes – Trig Part II Law of Sines and Cosines

Examples:

Law of Sines=

Law of Cosines=

Geometry Notes – 8.5 Angles of Elevation and Depression

Sketch and Label Parts:

Examples:

Geometry Notes – 8.6 Vectors

Vector:

Adding Vectors:

Compass Directions:

Geometry Notes – 9.1 Translations

Transformation:

Pre-Image:

Image:

Isometry:

Translation:

Labels: (PRIME)

Composition:

Geometry Notes – 9.2 Reflections

Reflection:

Opposite orientations (clockwise/counter):

Examples with Coordinates:

Geometry Notes – 9.3 Rotations

Rotation:

Orientation???

Examples:

Geometry Notes – 9.4 Reflection and Rotation Symmetry

Reflection-Symmetric Figures:

Activity 1:

Segment Theorem:

Side Switching Theorem:

Circle Symmetry:

Symmetric Figures Theorem:

Rotation Symmetry:

Point Symmetry:

Examples:

Geometry Notes – 9.5 Dilations

Dilation:

Enlargement or Reduction???

Examples:

Geometry Notes – 9.6 Composition of Reflections

Examples:

R F

Transformation if mirrors parallel:

Transformation if mirrors intersect:

Glide Reflection:

Example:

Geometry Notes – 9.7 Tessellations

Define Isometry:

Define Glide Reflection:

Example picture:

Mirror line and Vector must be parallel!

Flow Chart of Transformations:

What’s a Tessellation?

How does this relate to Geometry?

Master of Tessellations:

Geometry Notes – 10.1 Area of Parallelograms and Triangles

Formula:

Formula:

Examples:

Geometry Notes – 10.2 Area of Trapezoids, Rhombus and Kite

Formula:

Formula:

Examples:

Geometry Notes – 10.3 Area of Regular Polygons

Parts and Formula:

Examples:

Geometry Notes – 10.4 Perimeters and Areas of Similar Figures

Finding a similarity ratio:

Similarity ratio chart:

Examples:

Geometry Notes – 10.5 Trigonometry and Area

Parts and Trig:

Examples:

Area of Triangle with SAS:

What happens if you don’t know the apothem??

Examples:Geometry Notes – 10.6 Circles and Arcs

Picture and Parts:

Minor Arc:

Major Arc:

Adjacent Arcs:

Circumference:

Examples:

Concentric Circles:

Arc Length:

Examples:

Geometry Notes – 10.7 Areas of Circles and Sectors

Area of a Circle:

Examples:

Sector of a Circle:

Examples:

Segment of a Circle:

Picture (Triangle + Segment):

Examples:

Geometry Notes – 10.8 Geometric Probability

P(event) =

Different ways of reporting answer:

Examples:

Geometry Notes – 11.1 Space Figures and Cross Sections

Polyhedron:

Face:

Edge:

Vertex:

Example:

Euler’s Formula:

Net:

Examples:

Cross Sections:

Geometry Notes – 11.2 Surface Area of Prisms and Cylinders

Prism:

Bases:

Lateral Faces:

Finding Areas using a Net:

Lateral Area of a Prism:

Surface Area of a Prism:

Cylinder Net:

Lateral Area for a Cylinder:

Surface Area for a Cylinder:

Geometry Notes – 11.3 Surface Area of Pyramids and Cones

Lateral Area:

Surface Area:

Lateral Area:

Surface Area:

Geometry Notes – 11.4 Volume of Prisms and Cylinders

Volume:

Blocks example:

Volume of a Prism or Cylinder =

Examples:

Geometry Notes – 11.5 Volume of Pyramids and Cones

Shape Example:

Volume of a Pyramid or Cone =

Examples:

Cavalieri’s Principle:

Geometry Notes – 11.6 Surface Area and Volume of Spheres

Baseball Example:

Surface Area of a Sphere =

Volume of a Sphere =

Picture:

Example:

Geometry Notes – 11.7 Areas and Volumes of Similar Solids

Rectangular Prism Example:

*Area and Volume of Similar Solids:

Examples:

Geometry Notes – 12.1 Tangent Lines

Angle Example and Congruent Tangent Lines:

Is the line tangent to the circle example???

Pulley Example:

Geometry Notes – 12.2 Chords and Arcs

Facts about Chords and Arcs:

Examples:

Geometry Notes – 12.3 Inscribed Angles

Inscribed Angles in a Semicircle:

Quadrilateral Example:

Arcs formed by Chords and Tangents:

Inscribed Angle Theorem:

Other Pictures:

Geometry Notes – 12.4 Angle Measures and Segment Lengths

Secant Formulas:

1.

2.

3.

4.

5.

Secant: