High School Geometry
Preface
1
Reasoning and Proof
1.1
Axiomatic Development of Mathematics
1.1.1
Undefined Terms
1.1.2
Undefined Relations
1.1.3
Axioms Relating the Undefined Terms and Undefined Relations
1.1.4
Theorems
1.2
Logic and Propositional Calculus
1.2.1
Propositions and Compound Propositions
1.3
Reasoning
1.3.1
Inductive Reasoning
1.3.2
Deductive Reasoning
1.4
Logical Operations
1.4.1
Conditional Statements
1.4.2
Basic Logical Operations
1.4.3
Propositions and Truth Tables
1.4.4
Tautologies and Contradictions
1.4.5
Logical Equivalence
1.4.6
Algebra of Propositions
1.4.7
Conditional and Biconditional Statements
1.4.8
Arguments
1.4.9
Logical Implication
1.5
Sets and Basic Operations on Sets
1.5.1
Introduction
1.5.2
Sets and Elements
1.5.3
Universal Set, Empty Set
1.5.4
Subsets
1.5.5
Venn Diagrams
1.5.6
Set Operations
1.5.7
Algebra of Sets
1.5.8
Finite Sets, Counting Principles
1.5.9
Classes of Sets, Power Sets
1.5.10
Arguments and Venn Diagrams
1.6
Reason Using Properties of Algebra
2
Essentials of Geometry
2.1
Points, Lines, and Planes
2.2
Segments and Congruence
2.3
Midpoint and Distance Formulas
2.4
Angles
2.5
Angle Pair Relationships
2.6
Polygons
2.7
Prove Statements About Segments and Angles
2.8
Prove Angle Pair Relationshiops
3
Lines
3.1
Line and Angle Pairs
3.2
Parallel Lines and Transversals
3.3
Slopes of Lines
3.4
Write and Graph Equations of Lines
3.5
Perpendicular Lines
3.6
Intersection of Lines
4
Congruent Triangles
4.1
Triangle Properties
4.1.1
Classification
4.1.2
Triangle Sum Theorem
4.1.3
Exterior Angle Theorem
4.2
Apply Congruence in Triangles
4.2.1
Definitions
4.2.2
Third Angles Theorem
4.2.3
Properties of Congruent Triangles
4.3
Transformations and Congruence
4.3.1
Rigid Transformations
4.3.2
Non-Rigid Transformations
4.3.3
Perform Congruence Transformations
4.3.4
Perform Non-Congruence Transformations
4.4
Proving Triangles are Congruent
4.4.1
Side-Side-Side Congruence Postulate
4.4.2
Side-Angle-Side Congruence Postulate
4.4.3
Hypotenuse-Leg Congruence Theorem
4.4.4
Angle-Side-Angle Congruence Theorem
4.4.5
Angle-Angle-Side Congruence Theorem
4.5
Isoceles and Equilateral Triangles
4.5.1
Isosceles Triangles
4.5.2
Equilateral Triangles
5
Relationships within Triangles
6
Similarity
7
Right Triangles and Trigonometry
8
Quadrilaterals
9
Transformations
10
Circles
11
Measurements
12
Probability
References
Published with bookdown
High School Geometry
Chapter 4
Congruent Triangles
4.1
Triangle Properties
4.1.1
Classification
4.1.2
Triangle Sum Theorem
4.1.3
Exterior Angle Theorem
4.2
Apply Congruence in Triangles
4.2.1
Definitions
4.2.2
Third Angles Theorem
4.2.3
Properties of Congruent Triangles
4.3
Transformations and Congruence
4.3.1
Rigid Transformations
4.3.1.1
Translation
4.3.1.2
Reflections
4.3.1.3
Rotations
4.3.2
Non-Rigid Transformations
4.3.2.1
Dilations
4.3.3
Perform Congruence Transformations
4.3.3.1
Coordinate Notation
4.3.3.2
Matrix and Vector Notation
4.3.4
Perform Non-Congruence Transformations
4.3.4.1
Scalar Multiplation
4.4
Proving Triangles are Congruent
4.4.1
Side-Side-Side Congruence Postulate
4.4.2
Side-Angle-Side Congruence Postulate
4.4.3
Hypotenuse-Leg Congruence Theorem
4.4.4
Angle-Side-Angle Congruence Theorem
4.4.5
Angle-Angle-Side Congruence Theorem
4.5
Isoceles and Equilateral Triangles
4.5.1
Isosceles Triangles
4.5.1.1
Base Angles Theorem
4.5.1.2
Converse of Base Angles Theorem
4.5.2
Equilateral Triangles
4.5.2.1
Corollary of the Base Angles Theorem
4.5.2.2
Corollary to the Converse of Base Angles Theorem