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Geometry Final
All units 1-9 (add 10 when finished with the notes)
| Term | Definition |
|---|---|
| Classify | What category/group is it in? |
| Differentiate | How is it different than others in the same category? |
| Inductive Reasoning | Noticing patterns in data and making a conjecture based on the evidence. |
| Conjectures | Are not guaranteed to be true. |
| Conditional Statements | An 'if/then' statement (if A, then B). |
| Converse | If B, then A (not necessarily true). |
| Biconditional Statements | True in both directions (A⟺B). 'Drop if/then, add 'if and only if' between condition and conclusion.' |
| Deductive Reasoning | Uses a sequence of logical statements to prove a conclusion with 100% certainty. |
| Counterexample | Can disprove a conjecture. |
| Mathematical Proof | A rigorous argument with no loopholes or assumptions to justify that something is true. |
| Midpoint | Halfway between 2 endpoints of a segment. |
| Midpoint Formula | m = (x₁+x₂)/2, (y₁+y₂)/2 |
| Angles | Made of 2 rays that meet at a vertex. |
| Acute Angle | <90° |
| Right Angle | 90° |
| Obtuse Angle | >90° and <180° |
| Straight Angle | 180° |
| Angle Bisectors | Cut an angle in half. |
| Complementary Angles | Add to 90° |
| Supplementary Angles | Add to 180° |
| Vertical Angles | Congruent angles formed when two lines intersect. |
| Slope-Intercept Form | y=mx+b |
| Parallel Lines | Same slope. |
| Perpendicular Lines | Slopes are opposite reciprocals (e.g., b/a → -a/b). |
| Rigid Transformations | Translation (Shift), Reflection (Flip), Rotation (Turn). |
| Prime Notation | Used to make the image (△ABC→△A′B′C′). |
| Reflection across x-axis | (x,y)→(x,−y) |
| Reflection across y-axis | (x,y)→(−x,y) |
| Reflection across y=x | (x,y)→(y,x) |
| 90° CCW Rotation | (x,y)→(−y,x) |
| 180° Rotation | (x,y)→(−x,−y) |
| 270° CCW Rotation | (x,y)→(y,−x) |
| Composition of Transformations | When 2+ transformations occur in sequence (Order matters!). |
| Congruence Statement | △ABC≅△DEF means all corresponding sides and angles match up. |
| Triangle Sum Conjecture | Sum of angles in any △=180°. |
| Exterior Angle Conjecture | Exterior angle is equal to the sum of the 2 non-adjacent interior angles (a=b+c). |
| Congruence Shortcuts | SSS, SAS, ASA, AAS. |
| HL | Hypotenuse-Leg is used for right triangles. |
| CPCTC | Corresponding Parts of Congruent Triangles are Congruent. |
| Isosceles Triangle | Base angles are congruent. |
| Hierarchy of Quadrilaterals | Quadrilateral → Parallelogram → Rectangle/Rhombus → Square. |
| Properties of Parallelograms | Opposite sides/angles are ≅; consecutive angles are supplementary; diagonals bisect each other. |
| Rectangle Properties | Diagonals are congruent. |
| Rhombus Properties | Diagonals are ⊥ and bisect vertex angles. |
| Sum of Interior Angles of Polygons | 180(n−2). |
| Sum of Exterior Angles of Polygons | Always 360°. |
| Similar Figures | Same shape, different size. Angles stay the same. |
| Scale Factor (SF) | New/old (image/pre-image) |
| Dilation | Transformation that enlarges/reduces from a center point. |
| Shortcuts for Similarity | SSS~, AA~, SAS~. |
| Area Ratio | (Scale Factor)². |
| 45-45-90 Triangle | Legs x,x, Hypotenuse x√2. |
| 30-60-90 Triangle | Short leg x, Long leg x√3, Hypotenuse 2x. |
| Inverse Trig | Used to find the angle (e.g., sin⁻¹(ratio)=θ). |
| Circle Equation | (x−h)²+(y−k)²=r². |
| Tangent Lines | ⊥ to the radius at point of tangency. |
| Inscribed Angle | ½(intercepted arc). |
| Arc Length | θ/360 ⋅ 2πr. |
| Sector Area | θ/360 ⋅ πr². |
| Volume (V) | Space inside (measured in cubic units u³). |
| Surface Area (SA) | Sum of the area of all faces. |
| Prism Volume | Bh. |
| Cylinder Volume | πr²h. |
| Pyramid Volume | ⅓Bh. |
| Cone Volume | ⅓πr²h. |
| Sphere Volume | 4/3πr³. |
| Sine | O/H (Opposite/ Hypotenuse) |
| Cosine | A/H (Adjacent/Hypotenuse) |
| Tangent | O/A (Opposite/Adjacent) |
| Prism Surface Area Formula | SA = Ph + 2B |
| Cylinder Surface Area Formula | SA = 2πrh + 2πr² |
| Pyramid Surface Area Formula | SA = 1/2 Pl + B |
| Cone Surface Area Formula | SA = πrl + πr² |
| Sphere Surface Area Formula | SA = 4πr² |
| Variables in Prism Formula | P = Perimeter of base; h = height; B = Area of base |
| Variables in Cylinder Formula | r = radius; h = height |
| Variables in Pyramid Formula | P = Perimeter of base; l = slant height; B = Area of base |
| Variables in Cone Formula | r = radius; l = slant height |
| Variables in Sphere Formula | r = radius |
Created by:
AlanaMay
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