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Important Definitions and Facts in the Aims of Common Core Geometry
GUIDELINES FOR COMPLETING YOUR MARBLE NOTEBOOK.
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TOPIC A: Unknown Angles
Aim 1: Solve for unknown angles – Angles and Lines at a Point
A straight angle is
Adjacent angles are
Complementary angles Supplementary angles.
A linear pair of angles is
The sum of the adjacent angles about a point is
The sum of the adjacent angles on one side of a line is.
Vertical angles (vertically opposite angles) are
Vertical angles are
Aim 2: Solve for unknown angles - Transversals
If a transversal intersects two parallel lines, corresponding angles are
If a transversal intersects two parallel lines, alternate interior angles are
If a transversal intersects two parallel lines, same side interior angles are
An auxiliary line is
Aim 3: Solve for unknown angles – Angles in a Triangle
A two-dimensional figure is
An isosceles triangle is a triangle
Base angles of an isosceles triangle are
A scalene triangle is
An equilateral triangle is
An equiangular triangle is
A regular figure is
Each angle of an equilateral triangle
The sum of the angles of a triangle is
An exterior angle of a triangle is
An exterior angle of a triangle equals
Aim 4: Unknown Angle Proofs – Writing Proofs
A proof is
.
Deductive reasoning is
Reflexive Property: (words)
Transitive Property: (words)
Symmetric Property: (words)
Addition Property: (words)
Subtraction Property: (words)
Multiplication Property: (words)
Division Property: (words)
Substitution Property: (words)
Partition Property: (words)
TOPIC B: Basic Constructions
Aim 5: Construct an Equilateral Triangle I
A geometric construction is
Collinear points are
Non-collinear points are
Length of a segment:
Aim 6: Construct an Equilateral Triangle II
(Constructions based on constructing an equilateral triangle)
Aim 7: Copy and Bisect an Angle
An angle is
A half-plane is
An angle bisector is
Angles that form a linear pair are
Aim 8: Construct a Perpendicular Bisector
Two lines are perpendicular if
The midpoint of a segment
A segment bisector
The perpendicular bisector of a segment
Every point on the perpendicular bisector of a segment is.
Aim 9: Points of Concurrencies
Three or more lines are concurrent if
The circumcenter is
The incenter is
Aim 10: Unknown Angle Proofs – Proofs with Constructions [use of facts stated in Aims 1-4, 7]
Aim 11: Unknown Angle Proofs – Proofs of Facts
A proof is
A postulate is
A theorem is.
If two lines are perpendicular to the same line,
If two lines are cut by a transversal such that alternate interior angles are =,
If two lines are cut by a transversal such that corresponding angles are =,
If two lines are cut by a transversal such that same side interior angles are supplementary,