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Geometry
10th grade Carly
| Question | Answer |
|---|---|
| What is reflexive property | a=a |
| What is symmetric property | if a = b then b = a |
| What is transitive property | if a = b and b = c then a = c |
| Commutative property of multiplication | a x b = b x a |
| Commutative property of addition | a + b = b + a |
| Associative property of multiplication | (ab)c = a(bc) |
| Addition property of equality | if a = b then a + c = b + c |
| Subtraction property of equality | if a = b then a - c = b - c |
| Multiplication property of equality | if a = b then a x c = b x c |
| Division property of equality | if a = b then a/c = b/c |
| Distributive property | a(b + c) = ab + ac |
| Acute angle | an angle that measures less than 90 degrees |
| right angle | an angle that measures exactly 90 degree |
| Obtuse angle | an angle that measures between 90 and 180 degrees |
| Complimentary angles | angles whose measure adds up to 90 degrees |
| Straight Angle | an angle that measures exactly 180 degrees |
| Supplementary Angles | Angles whose measure adds up to 180 degrees |
| Vertical angles | angles opposite one another at the intersection of two lines |
| Adjacent angles | Angles that have a common side and a common vertex (corner point) |
| Vertex | a point where two or more straight lines meet |
| Congruent Angle | Angles that have the same measure |
| There is exactly one line | Through any two points |
| There is exactly one plane | Through any three noncollinear points |
| Two points | A line contains at least |
| three noncollinear points | A plane contains at least |
| Noncollinear points | points that do not all lie on same line |
| Collinear points | points that all lie on the same line |
| Reflexive property of congruence | Line AB is congruent to line AB |
| Symmetric Property of congruence | If line AB is congruent to line CD, then line CD is congruent to line AB |
| Transitive Property of congruence | if line AB is congruent to line CD and line CD is congruent to line EF, then line AB is congruent to line EF |
| Supplement Theorem | If two angles form a linear pair, then the are supplementary angles |
| Complement Theorem | If the on common sides of two adjacent angles form a right angle, then the angles are complementary angles |
| If two angles are vertical angles | Then they are congruen |
| Congruent | All right angles are |
| Congruent adjacent angles | Perpendicular lines form it |
| Perpendicular lines intersect to form | four right angles |
| Theorem | a statement that can be proven |
| Transversal | a line that cuts a pair of parallel lines resulting in the formation of congruent and supplementary angle relationships |
| Corresponding angles | pairs of angles formed by two lines and a transversal that makes an F pattern |
| Angle bisector | A ray that begins at the vertex of an angle and divides the angle into two angles of equal measure |
| Segment bisector | a ray, line or segment that divides a segment into two parts of equal measure |
| Alternate Interior Angles | If transversal intersects 2 parallel lines, then alternate interior angles are congruent |
| Same side Exterior Angles | If a transversal intersects 2 parallel lines, then alternate exterior angles are congruent |
| Converse of the Corresponding Angles | Proving lines are parallel given angle relationship |
| Converse of the Alternate Interior Angles | if 2 lines and a transversal form alternate interior angles that are congruent, then the 2 lines are parallel |
| Converse of the Alternate Exterior Angles | If 2 lines and a transversal form alternate exterior angles that are congruent, then the 2 lines are parallel. |
| Converse | Proves lines are parallel (proving lines are parallel given angle relationships) |
| midpoint | The middle point of a line segment |
| Perpendicular lines | Lines that meet at a right angle |
| Perpendicular Bisector | A perpendicular bisector is a line that cuts a line segment connected by two points exactly in half by a 90 degree angle |
| Isosceles Triangle | A triangle with two equal sides |
| Equilateral Triangle | a triangle in which all three sides are equal |
| Segment Addition Postulate | if B is between A and C, then AB + BC = AC. The converse is not necessarily true. |
| Interior angles | Inside parallel lines |
| Exterior angles | Outside Parallel lines |
| Alternate | Opposite sides of the transveral |
| Same side | Same side of the transversal |
| Corresponding | Same/similar position on parallel lines AND transversal |
| Proof | A convincing argument that something is true |
| Inductive Reasoning | Observing data looking for conclusions (conjecture) |
| Deductive Reasoning | Conclusion comes from facts already proven |
| Theorem | Conjecture that is proven |
| Methods of geometric proofs | two column, paragraph proofs, flow chart proofs and coordinate proofs |
| What are 4 premises used as types of reasons to statement? | Definitions, postulates, theorem, algebraic properties, properties of equality or congruence |
| What is used for actual values, numbers and measurements: | Properties of Equality for Real Numbers |
| What is used for shapes, figures, parts of shapes and parts of figures? | Properties of Congruence |
| How to prove angles are congruent or supplementary given parallel lines | (Congruents): Corresponding Angles Theorem, Alternate interior Angles Theorem, Alternate Exterior Angles, Vertical Angles Theorem and (Supplementary) by Same Side Interior; Linear Pair of Angles Theorem, |
| Ways to Prove Parallel Lines given congruent or supplementary Angles | (Congruents): Converse of Corresponding Angles, Converse of Alternate Interior Ang, Converse of Alternate Exterior Ang, (Supp) Converse of Same Side Interior Ang, Converse of linear Pair of Ang, Transitive Prop. of parallel, Prop. of Perpendiclar |
Created by:
hgkaduson