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:
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
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 – 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 – 5.2 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 – 6.2 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 – 7.3 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 – 4.5 Isosceles and Equilateral Triangles
Isosceles Triangle Parts and Theorems:
Equilateral Theorems:
Examples:
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 – 8.3/8.4 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 – 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
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:
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
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:
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 – 12.3 Inscribed Angles
Inscribed Angles in a Semicircle:
Quadrilateral Example:
Arcs formed by Chords and Tangents:
Inscribed Angle Theorem:
Other Pictures: