BC: Cats are so intelligent...
FC: A Student's Vocabulary Guide to Honors Geometry | By: Rehnuma Khan and Maryam Haider
1: Table of Contents | Logic... pg Geometry Basics Triangle Proofs Parallel Lines Quadrilaterals Coordinate Geometry Systems of Equations Similarity Right Triangle Proportions Triangle Inequalities Exponentials Logarithms Circles
2: LOGIC | Biconditional- a compound statement that uses "if and only if". Only true when both statements have the same truth value (false or true). Chain Rule- A rule of logic that states that if a is true then b is true, and if b is true then c is true. Therefore, if a is true then c is true Closed Sentence- A sentence that can be judged true or false Compound Statement- Joining two sentences together using a connective, i.e. and Conclusion- The part of the conditional that follows "then" Conditional- A compound statement that uses if and then. It is only false if a true hypothesis follows a false conclusion Conjunction- A compound statement using "and" that is only true when both statements are true Contrapositive- The switching and negation of the hypothesis and conclusion. It always has the same truth value as the original conditional.
3: Converse-The switching of a conditional and a hypothesis in a conditional statement Disjunction- A compound statement using "or". Only false if both statements are false Formal Proof- A series of mathematical sentences, theorems, axioms, and postulates used to prove the validity of a statement. Hypothesis- The part of the conditional that follows "if" Inverse- When you negate both the hypothesis and conclusion of a conditional statement Law of Contrapositives- The converse and inverse of a statement (contrapositive) has the same truth value as the original statement Law of Detachment- If p -> q is true and q is true, then p must be true Law of Disjunctive Inferences- Given the true statements p or q and ~q, then p must be true Law of Modus Tollens- If p -> q and ~q are true statements, then ~p must be true
4: Mathematical Sentence- A sentence that states a fact, i.e. 1+2=3 Negation- Always has the opposite truth value as the original statement Phrase- An incomplete sentence, i.e. 1+2 Open Statement- A sentence that includes a variable such as "it" or "x" Statement- A sentence that states a fact Tautology- When the final column of a truth table has all true values Testing the Validity- When a sentence can be proved true or false using reasoning Truth Table- A table used to evaluate the validity of each expression with different combinations Truth Value- How true or false a proposition or statement is
5: Geometry Basics | AAS (angle angle side)- Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles. Angle bisector- A ray whose endpoint is the vertex of the angle and which divides the angle into two congruent angles. ASA (angle side angle)- Two angles and a included side of a triangle make these two triangles congruent. Line Bisector- A line, ray or segment which cuts another line segment into two equal parts. Midpoint- The middle point of a line segment, it is equidistant from both endpoints. Parallel Line- Lines that never intersect Perpendicular Line- Two lines which intersect to form right angles
6: Perpendicular bisector- A line which cuts a line segment into two equal parts at 90 Reflexive property- A quantity is congruent (equal) to itself SAS (side angle side)- Two triangles have two sides and the included angle equal to one another, then they are congruent to each other. SSS (side side side)- Three sides of one triangle are congruent to three sides of another triangle, then these two triangles are congruent. Vertical angles- Angles opposite each other when two lines cross, and are congruent to each other
7: Triangle Proofs | Addition Postulate- If equal quantities are added to equal quantities, then the sums are equal Altitude- A line segment that is drawn from the vertex of a triangle to the base, and it is perpendicular to the base of a triangle Complementary Angles- Two angles which have a sum of 90 degrees Equilateral Triangle- All three sides are congruent, and each angle is 60 degrees Hypotenuse Leg- When the hypotenuses and legs of two triangles are congruent, the triangles can be proved congruent using this theorem rather than SSA Isosceles Triangle- Two sides and two angles of the triangle are congruent Linear Pairs- Adjacent angles which total 180 degrees Median- A line segment that is drawn from the vertex of a triangle to the midpoint. It bisects the side to which it is drawn.
8: Scalene Triangle- No sides or angles are congruent Subtraction Postulate- If equal quantities are subtracted from equal quantities, then the differences are equal Supplementary Angles- Two angles which have a sum of 180 degrees Transitive Property- If a=b and b=c, then a=c Vertex Angle- The angle formed by two legs of a triangle that is opposite the base
9: Parallel Lines | Alternative interior angles- Pairs of angles on opposite sides of the transversal but inside the two lines Alternative exterior angles- Pairs of angles on opposite sides of the transversal but outside the two lines Continued ratio - Corresponding angles- Angles in matching corners of a transversal Decagon- A polygon with 10 sides Dodecagon- A polygon with 12 sides Hexagon- A polygon with 6 sides Ngon- A polygon with n sides. Pentagon- A polygon with 5 sides Regular Polygon- A polygon with all sides and all angles equal Same side interior angles- Inside the parallel lines, and on the same side of the transversal. Transversal- A line that crosses at least two other lines. Octagon- A polygon with 8 sides
11: Quadrilaterals | Consecutive Angles- Angles that occur one after the other Diagonals- Line segments that are drawn from one vertex of a figure to the opposite vertex Isosceles Trapezoid- A quadrilateral in which: 1. The legs are congruent 2. There is only one pair of parallel sides 3. Diagonals are congruent 4. Base angles are congruent Parallelogram- A quadrilateral in which: 1. Opposite sides are parallel 2. Opposite sides are congruent 3. Opposite angles are congruent 4. Diagonals bisect each other 5. Consecutive angles are supplementary Rectangle- A quadrilateral in which: 1. The diagonals are congruent 2. All angles equal 90 degrees 3. The properties of a parallelogram apply
12: Rhombus- A quadrilateral in which: 1. The properties of a parallelogram apply 2. All sides are congruent 3. Diagonals bisect the angles 4. The diagonals are perpendicular Squares- A quadrilateral in which: 1. The properties of a parallelogram apply 2. The properties of a rhombus apply 3. The properties of a rectangle apply Trapezoid- A quadrilateral in which there is only one pair of opposite parallel sides
13: Coordinate Geometry | Distance formula- Midpoint formula- Negative slope- A slope of a curve that is less than zero, representing a negative or inverse relationship between two variables No slope- This is a term which should probably be avoided, since it could be interpreted to mean "slope of zero" or "undefined Positive slope- a slope of a curve that is greater than zero, representing a positive or direct relationship between two variables Pythagorean Theorem-
14: Quadrants- Undefined- When there is a vertical line that has different y points, but the same x point. X- axis- The horizontal axis in a plane coordinate system Y- axis- The vertical axis in a plane coordinate system. Zero slope- When there is a horizontal line that has different x points, but the same y point.
15: Systems of Equations | Axis of Symmetry- A line through a parabola which divides it symmetrically Formula: x= -b/2a Center- The middle of a circle from where every outer point is equidistant Circle- A geometric figure in which an infinite number of points are equidistant from a center Diameter- A measurement of the length of a circle through the center Equation of a Circle- Expressed in the standard or center-radius forms: Standard: x^2+ y^2+ Cx+ Dy+ E= 0 Center-Radius: (x-h)^2+ (y-k)^2= 0 Linear Equation- When graphed, linear equations produce straight lines with a specific slope according to the equation, y=mx+b, in which m represents slope
16: Parabola- A curved figure formed by quadratic equations which are symmetrical Quadratic Equation- ax^2+ bx+ c Radius- A line from the center of a circle to any point on the circumference; half the diameter Solutions- A set of numbers that satisfy the given equation Turning Point- The point at which a parabola curves Vertex- The highest or lowest point on the parabola through which it is symmetrical
17: Similarity | AA Theorem- The theorem used to prove two triangles are similar because the angles are congruent Corresponding Parts- Angles, sides or vertices which are in the same location on figures that are congruent or similar; their parts will be in proportion Extremes- Ratio- Scale Factor- Means - Proportions - Ratio of volumes - Ratio of Areas - Ratio o perimeters - Ratio of similitude -
19: Altitude Rule- The length of the altitude is the mean proportional between the segments of the hypotenuse Geometric Mean- Synonymous to "mean proportional" Leg Rule- The legs of a triangle are the mean proportional between the hypotenuse and the projections Mean Proportional- A proportion in which the means are the same value Projection- a part of the hypotenuse created when an altitude divides the hypotenuse | Right Triangle Proportions
21: Triangle Inequalities | Equality- Being equal in amount Exterior Angle Theorem- The exterior angle is equal to the sum of the remote interior angles Inequality- When the amounts vary with relationships expressed as: "less than" or "greater than" Largest Angle- The angle with the greatest amount that is opposite the longest side Longest Side- The side that is the longest in length and is opposite the largest angle Non-adjacent Angle- Angles that are not next to the given angle Remote Interior Angles- Angles that are remote to a given exterior angle Smallest Angle- The smallest angle is opposite the shortest side Shortest Side- The shortest side is opposite the smallest angle
22: Logarithms | Logarithmic Function- The logarithm of a number to a given base is the power or exponent to which the base must be raised in order to produce Asymptote- A line that a graph gets closer and closer to, but never touches or crosses. Common Logarithm- A logarithm to the base of ten. Antilogarithm- The opposite of log, to obtain an antilogarithm you have to raise the base to the power the antilog is equal to. Natural Logarithm- A logarithm in which the base is the irrational number Power Rule - This is the rule used to indicate the answer to a logarithm that has its answer raised to a power. Product- The result of multiplying a set of numbers or expressions.
24: Circles | Complete the Square- A method to find the roots of a quadratic equation if factoring does not work. 1.Move the "c" term to the other side 2. Take half the "b" term and square it. Then, place the resulting number in place of "c", and add it to the other side and square root it. Put a + or - sign in front of the radical. 3. Make the equation into a perfect square by placing half the b term after "x" so it should be similar to (x-w)^2. Solve. | Center-Radius Form- An equation to express information about the graph of a circle. (x-h)^2 + (y-k)^2= r^2 H and K represent the x and y coordinates of the center. R represents the radius | General Form- An equation that expresses information about the graph of a circle, also known as standard form. Can be changed to center-radius form by rearranging the equation and completing the square. x^2+y^2+Cx+Dy+E=0
25: Factoring by Grouping- A method of factoring a polynomial 1. Find the factors of the middle term which equals the sum of the last term 2. Replace the middle term with the two new factors 3. Factor the first two terms, then factor the second two 4. Notice that the two terms in parenthesis are the same, so they represent a single term. Combine the two numbers or variables on the outside to form a second term. Double Distribute to check. | Factoring Perfect Cubes- A method of factoring perfect cubes 1. Take the cube root of the term and put it into parenthesis 2. Factor the remaining term using the acronym "SOAP". The sign of the first term will be the same, the second one will have the opposite sign, and the third will always be positive.
26: Sources: -Google -Studystack.com -Dictionary.com -Mrs. Salke's notes -Themathpage.com