Definition / Postulates / Theorems Checklist

Transcription

1 3 undefined terms: point, line, plane Definition / Postulates / Theorems Checklist Section Definition Postulate Theorem 1.2 Space Collinear Non-collinear Coplanar Non-coplanar Intersection 1.3 Segment Ruler postulate Ray Segment addition postulate (SAP) Endpoint Opposite rays Length (distance) of a segment Coordinate Postulate (axiom) Congruent Congruent segments Midpoint Bisector Between 1.4 Angle Protractor postulate Vertex Angle addition postulate (AAP) Side Congruent angles Adjacent angles Angle bisector Right angle Measure of an angle Acute angle Obtuse angle Straight angle 1.5 Theorem 5 postulates on page 23 3 theorems on page 23 One and only one Unique Exist determine 2.1 Conditional statement Conditional Hypothesis Conclusion If-then Impies Only if Converse Biconditional If and only if

2 Counter-example 2.2 All the properties of equality on p 37 All the properties of on p 37 Other algebra properties 2.3 Midpoint Th (MPT) Angle bisector Th (ABT) 2.4 Complementary angles Vertical angles Th (VAT) Supplementary angles Vertical angles 2.5 Perpendicular lines 3 theorems from p The Supplement Th (Th2-7) The Complement Th (Th 2-8) 3.1 Parallel (//) lines Skew lines // planes A line // to a plane Transversal Exterior angles Interior angles Alternate interior angles (AIA) Same-side interior angles (SSIA) Corresponding angles (CA) 3.2 The PCA postulate (Post. 10) The PAIA Th (Th 3-2) The PSSIA Th (Th 3-3) 1 more theorem on p The CAP postulate (Post. 11) The AIAP Th (Th 3-5) The SSIAP Th (Th 3-6) 4 more theorems on p Triangle Δ-angle sum Th (Th 3-11) Vertex (of a Δ) 4 more corollaries on p 94 Side (of a Δ) The Exterior Angle Theorem (EAT) (Th 3-12) Scalene Δ Isosceles Δ Equilateral Δ Acute Δ Obtuse Δ Right Δ Equiangular Δ Auxiliary line Exterior angle of a Δ Interior angle of a Δ Remote interior angle of a Δ 3.5 Polygon n-gon Interior Angles Sum Th. Convex polygon n-gon Exterior Angles Sum Th. Concave polygon diagonal Names of polygon with 3 to 10

3 sides 3.6 Inductive reasoning Deductive reasoning 4.1 Congruent figures Corresponding sides of figures Corresponding angles of figures Corresponding parts of figures Δs (CPCTC) 4.2 SSS SAS ASA 4.3 A line perpendicular to a plane 4.4 Base of an isosceles Δ The Isos. Δ Th. (ITT) (Th. 4-1) Legs of an isosceles Δ The converse of ITT (Th 4-2) Base angles of an isosceles Δ 4 more corollaries on p Vertex angle of an isosceles Δ 4.5 Hypotenuse of a right Δ AAS Legs of a right Δ HL 4.7 Median of a Δ The bisector Th (PBT) (Th. 4-5) Altitude of a Δ The converse of PBT (Th 4-6) Perpendicular bisector of a segment 2 more theorems from p 154 (skip) Distance from a point to a line Orthocenter Incenter Circumcenter centroid 5.1 Parallelogram 3 theorems from p from p from p from p 178 (Th 5-10) The Midline Theorem (Th 5-11) 5.4 Rectangle 6 from p 185 Rhombus square 5.5 Trapezoid Isos. Trap. Th (Th 5-18) Legs of a trapezoid Median of Trap. Th (Th. 5-19) Bases of a trapezoid Base angles of a trapezoid Isosceles trapezoid Median of a trapezoid 7.1 Ratio Proportion 7.2 Mean-Extreme Property Other Properties of Proportion 7.3 Similar polygons Similar Triangles Scale factor

4 7.4 AA~ Postulate 7.5 SAS~ Th SSS~ Th 7.6 Triangle Proportionality Th (TPT) Collorary of TPT Triangle Angle Bisector Th (skip) 14.1 Image Preimage Mapping One-to-one mapping Function One-to-one function Transformation Rigid motion Isometry Congruence mapping 14.2 Reflection Line (axis) of reflection 14.3 Translation Glide reflection 14.4 Rotation Center of rotation Half-turn 14.5 Dilation Expansion Contraction Similarity mapping 8.1 Geometric mean Right Δ Geom. Mean Th - corollary 1 and Hypotenuse of a right Δ Legs of a right Δ Pythagorean Th. 8.3 Pythagorean Triples Converse of Pythagorean Th Δ Th Δ Th SOH-CAH-TOA 8.7 Angle of elevation Angle of depression 9.1 Circle Center of a circle Radius of a circle Chord Diameter Secant (line) Tangent (line)

5 Point of tangency Sphere Congruent circles (spheres) Concentric circles (spheres) Polygon inscribed in a circle (inscribed polygon) Polygon circumscribed about a circle (circumscribed polygon) 9.2 Inscribed circle Circumscribed circle Common internal tangents 2 Theorems and 1 corollary Common external tangents Tangent circles (internal or external) 9.3 Central angle Arc Addition Postulate 1 theorem Arc Minor arc / major arc intercepted arc semicircle Congruent arcs theorems 9.5 Inscribed angles Inscribed Angle Theorem - 3 corollaries Theorem on p 352 (Tangent Secant Angle Theorem) Chord Theorem 2-Secant Theorem 2-Tangent Theorem Tangent-Secant Theorem Chord Power Theorem 2-Secant Power Theorem Tangent-Secant Power Theorem