Please enable JavaScript.
Coggle requires JavaScript to display documents.
Honors Geometry Semester 1 (Unit 2: Reasoning and Proof (Proving angle…
Honors Geometry Semester 1
Unit 1: Tools of Geometry
Angle Constructions
Copy an Angle
Bisect an angle
Construct an angle two times larger
Construct an angle whose measure is equal to the sum of the measures of the angles given.
Construct an angle whose measure is equal to the difference of the measures of the angles given.
Construct 30, 45, 60, 90 angles
Line Constructions
Construct a line segment congruent to each given line segment.
Construct a line segment whose length is equal to the sum of the lengths of the given line segments.
Construct a line segment whose length is equal to the difference of the lengths of the given line segments.
Construct a line segment the given number of times longer than a segment.
Divide each line segment into the number of equal parts specified.
Construct the perpendicular bisector
Locate the midpoint
Construct a line segment perpendicular to the segment
Construct a line segment through the given point parallel
Unit 2: Reasoning and Proof
Logic
A statement is a sentence that is either true or false
Negation of a statement has the opposite meaning
Two or more statements joined by the word and or or form a compound statement
A conjunction is true only when both statements that form it are true.
A compound statements that uses the work or is called disjunction
Truth Tables
Conditional Statements
Conditional statement is a statement that can be written in if then form
Related Conditions: Converse, inverse, contrapositive
Logically equivalent
Deductive reasonning
Deductive reasoning uses facts, rules, definition, or properties to reach logical conclusions from given statements
Law of detachment
Law of syllogism is another form of deductive reasoning
Postulates and Paragraph proofs
A postulate or axiom is a statement that is accepted as true without proof
Paragraph proof (informal proof)
Algebraic Proof
An algebraic proof is a proof that is made up of series of algebraic statments
Two column proof (formal proof)
Proving Segment Relationships
Ruler postulate
Segment Addition Postulate
Properties of segment congruence (reflexive, symmetric, transitive)
Transitive property of congruence
Proving angle relationships
Protractor Postulate
Angle Addition Postulate
Supplement Theorem
Complement Theorem
Properties of Angle congruence
Congruent Supplements theorem
Congruent complements theorem
Inductive Reasoning and Conjecture
The false example is called a counterexample, and it can be a number, a drawing or a statement
A concluding statement reached using inductive reasoning is called a conjecture
Inductive is reasoning that uses a number of specific examples to arrive at a conclusion
Unit 3: Parallel and Perpendicular lines
Parallel Lines and transversals
parallel lines/skew lines/Parallel planes
Transversal
Interior angles, exterior angles, consecutive interior angles, alternate interior angles, alternate exterior angles, corresponding angles
Alternate interior angle theorem / Consecutive Interior angles theorem / Alternate Exterior Angles theorem
Slopes of lines
Slope: change of y / change of x
Parallel and perpendicular lines
Equations of lines
Slope intercept form
Point slope form
Horizontal and vertical line equations
Proving Lines Parallel
Converse of Corresponding angles postulate
Parallel postulate
Alernate exterior angle converse / consecutive interior angles converse / alternative interior angles converse / perpendicular transversal converse
Perpendicular and distance
Distance between a point and a line
Perpendicular postulate
Distance between parallel lines
Two lines equidistant from a third
Unit 4: Triangle Congruence
Classifying Triangles
Acute / equiangular / obtuse / right
Equilateral / isosceles / scalene
Angles of triangles
Triangle angle sum theorem
Exterior angle theorem
Flow proof
Triangle angle-sum corollaries
Congruent Triangles
Congruent polygons
corresponding parts
Definition of congruent polygons
Third angle theorem
Properties of triangle conguruence
Proving Triangles congruent-SSS, SAS
Side-Side-Side (SSS) congruence
Side-Angle-Side (SAS) congruence
Proving triangles congruent - ASA, AAS
Angle-side-angle (ASA) congruence
Included side
Angle-Angle-Sude (AAS) Congruence
Angle-Angle-Side theorem
Isosceles and Equilateral Triangles
vertex angle / base angle / legs of an isosceles triangle
Isosceles triangle theorem
Converse of isosceles triangle theorem
Equilateral Triangle Corollaries
Congruence Transformation
A transformation is an operation that maps an original geometric figure, the pre-image, onto a new figure called the image
Congruence transformation(isometry)
Reflection / translation / rotations
Triangles and Coordinate proof
coordinate proofs use figures in the coordinate plane and algebra to prove geometric concepts
Unit 5: Relationships in Triangles
Bisectors of triangles
If a bisector is also perpendicular to the segment, it is called a perpendicular bisector
Perpendicular bisector theorem
Converse of the perpendicular bisector
Concurrent lines / point of concurrency
Circumcenter Theorem
Angle bisector theorem / converse of the angle bisector theorem
Incenter theorem
Medians and altitudes of triangles
Centroid theorem
median
centroid
Orthocenter
Perpendicular bisector - circumcenter / angle bisector - incenter / median - centroid / altitude - orthocenter
Inequalities in one triangle
Definition of inequality
Exterior angle inequality
Comparison / transitive / additional / subtraction property
Exterior angle inequality
Angle side Relationships in triangles
Indirect proof
indirect reasoning (proof by contradiction)
The triangle inequality
triangle inequality theorem
Inequalities in two triangles
Hinge theorem
converse of the hinge theorem