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Geometry
Regents Review
97
Mathematics
06/18/2012

Term
 Negation: Symbol? Word? Rule?
Definition
 ~, not, Opposite Truth Value
Term
 Conjunction: Symbol, Word, Rule?
Definition
 /\, and, True When Both Are True
Term
 Disjunction: Symbol? Word? Rule?
Definition
 V, or, True If Least One is True
Term
 Conditional: Symbol? Word? Rule?
Definition
 ->, If... Then..., Always True Except If T->F
Term
 Biconditional: Symbol? Word? Rule?
Definition
 <-->, "If and only if", True If Both Have Same Truth Value
Term
 Negating a Conditional: Rule? Words?
Definition
 Negate the Sentence as a Whole (i.e. ~(p->q),It is not true that if..., then...
Term
 Negating Universal Quantifier: Words?, Rule?
Definition
 All, Every1)Change universal to existential2)Negate the sentence
Term
 Negating Existential Quantifier: Words?, Rule?
Definition
 Some1)Change existential to universal2)Negate the sentence
Term
 Rule of Converse?
Definition
 Switch Order
Term
 Rule of Inverse?
Definition
 Insert Negation to Both Terms
Term
 Rule of Contrapositive?
Definition
 Switch Order and Negate Both
Term
 Copy a Line Segment Rules
Definition
 1)Draw a straight line2)Put compass on segment endpoints3)Copy the segment onto straight line
Term
 Draw Perpendicular Bisector Rules
Definition
 1)Put compass open on one point, more then halfway open2)Create X marks the spots from points3)Connect the two X's
Term
 Copy an Angle
Definition
 1)Draw a ray with the ruler2)Draw an arc on the angle3)Put compass points on intersections4)Create X Marks the Spot on the Ray5)Connect ray point and X
Term
 Draw Angle Bisector
Definition
 1)Draw an arc through the angle2)Create X marks the spot from the intersections between angle and arc3)Connect point on ray and X
Term
 Draw a line perpendicular to a line through a point
Definition
 1)Draw arc that intersects line twice from the point2)Create X marks the spot from intersections between line and arc3)Connect X and point
Term
 Complementary Angles Sum?
Definition
 90 degrees
Term
 Supplementary Angles Sum?
Definition
 180 degrees
Term
 What are vertical angles?
Definition
 Non adjacent angles formed by two intersecting angles
Term
Definition
 Angles that share a vertex and a ray
Term
 Congruent Angles in Parallel Lines Cut by a Transversal?
Definition
 Corresponding Angles, Alternate Interior and Exterior Angles
Term
 Number of degrees in a triangle?
Definition
 180 degrees
Term
 Acute triangle properties?
Definition
 All angles are acute
Term
 Obtuse triangle properties?
Definition
 One angle is obtuse, others are acute
Term
 Right triangle properties?
Definition
 a^2+b^2=c^2, One angle is right, others are acute, Pythagorean Triplets = (3,4,5) (5,12,13) (8,15,17)
Term
 Scalene triangle properties?
Definition
 No sides or angles congruent
Term
 Equilateral triangle properties?
Definition
 All sides congruent, angles are 60 degrees
Term
 Isosceles triangle properties?
Definition
 Two Base Angles Opposite Congruent Sides are Congruent, Two Sides are Congruent, Median is the Same as Angle Bisector and Altitude to the Base
Term
 Triangle Sides Theorem?
Definition
 The sum of two sides must be greater than the third side
Term
 Sides and Angles in a Triangle Theorem?
Definition
 The longest side of a triangle of a triangle is opposite the largest angle, the shortest side of a triangle is opposite the shortest side
Term
 Exterior Angle Theorem?
Definition
 The exterior angle is equal to the sum of the two remote interior angles
Term
 Altitude in a Triangle Is?
Definition
 Line drawn to a side from an angle perpendicular to that side
Term
 Median in a Triangle Is?
Definition
 Line drawn to a side from an angle that bisects that side
Term
 What does "Peanut Butter Cookies Always Bake In Mom's Ceramic Antique Oven" Mean?
Definition
 Perpendicular Bisector CircumcenterAngle Bisector IncenterMedian CentroidAltitude Orthocenter
Term
 Similar Polygons have?
Definition
 Same shape but different size, Triangles are Congruent if Their Angles are Congruent
Term
 Similar Triangle Properties?
Definition
 1)Corresponding sides are in proportion2)Medians,altitudes, perimeters are proportionate with ratios of sides3)Area is equal to the square of the ratios of the lengths of the corresponding sides
Term
 What happens if a segment joins the midpoints of two sides of a triangle?
Definition
 The segment is parallel to the third side and is half the length of the third side
Term
 What happens if a segment is parallel to the third side of a triangle?
Definition
 Two similar triangles are formed
Term
 5 Properties of a Parallelogram?
Definition
 1) Opposite sides are parallel2) Opposite sides are congruent3) Opposite angles are congruent4) Consecutive angles are supplementary5) Diagonals bisect one another
Term
 2 Properties of a Rectangle?
Definition
 * Has all parallelogram properties1) Congruent diagonals2) All angles are right angles
Term
 3 Properties of a Rhombus?
Definition
 * Has all parallelogram properties1) Diagonals are perpendicular2) Diagonals bisect the angles3) All 4 sides are congruent
Term
 Properties of a Square?
Definition
 EVERYTHING in the parallelogram family
Term
 1 Property of a Trapezoid?
Definition
 1) One and only one pair of opposite sides are parallel
Term
 3 Properties of Isosceles Trapezoids?
Definition
 * Has only one pair of sides parallel1) Congruent diagonals2) Base angles are congruent3) Non parallel sides are congruent
Term
 Property of a Right Trapezoid?
Definition
 * Has one pair of sides parallel1) One leg is perpendicular to base
Term
 What happens if two non parallel sides' midpoints are joined in a trapezoid?
Definition
 The segment is parallel to the third side and is half the sum of the two bases.
Term
 Methods for Proving Triangles Congruent?
Definition
 SSS, AAS, ASA, SAS, HLNOT ASS, AAA
Term
 If two triangles are congruent then their corresponding parts are...
Definition
 Congruent. CPCTC
Term
 Methods for Proving Triangles Similar?
Definition
 AA, SAS*, or SSS*The sides must be in a ratio as stated in the given
Term
 Slope Formula?
Definition
 [image]
Term
 Distance Formula?
Definition
 [image]
Term
 Midpoint Formula?
Definition
 [image]
Term
 Slope Intercept Form of a Line?
Definition
 [image]
Term
 Point Slope Form of a Line?
Definition
 [image]
Term
 Equation of a circle?
Definition
 [image]
Term
 Equation of a parabola?
Definition
 [image]
Term
 Relationship between central angle and arc?
Definition
 They are congruent
Term
 Relationship between inscribed angle and its arc?
Definition
 Angle=1/2 arc
Term
 Chord Chord Angle is equal to?
Definition
 Sum of intercepted arcs/2
Term
 Tangent Chord Angle?
Definition
 Angle=1/2 intercepted arc
Term
 Angle whose vertex is outside circle is equal to?
Definition
 Angle=1/2 (larger arc - smaller arc)
Term
 Common external tangents and common internal tangents of a given circle are...
Definition
 Congruent, unless you are dealing with intersecting circles and common internal tangents, no said tangent exists
Term
 If a chord intersects a chord, what is the relationship between the two segments?
Definition
 Part of One Chord x Part of the Same Chord = Part of the Other Chord x Part of That Chord (Piece)(Piece)=(Piece)(Piece)
Term
 If two secants intersects a circle from a common exterior point, what is the relationship between the segments?
Definition
 Outer Part of Segment x Whole Segment = Outer Part of Other Segment x Whole Segment (Whole)(Piece)=(Whole)(Piece)
Term
 If a tangent and a secant are drawn from the same exterior point, what is the relationship between the segments?
Definition
 Tangent x Tangent = Outer Piece of Segment x Whole Segment
Term
 Locus of points from a point?
Definition
 A circle
Term
 Locus of points from two points?
Definition
 A line that would perpendicularly bisect a line joining the two theoretical points
Term
 Locus of points from a line?
Definition
 Two parallel lines
Term
 Locus of points from two parallel lines?
Definition
 A third parallel line
Term
 Locus of points from two intersecting lines?
Definition
 2 Angle Bisectors
Term
 Reflections over the x-axis?
Definition
 (x, -y) Negate y
Term
 Reflection over the origin?
Definition
 Negate both x and y
Term
 Translation?
Definition
 Add x values and y values
Term
 Dilation?
Definition
 Multiply x values and y values
Term
 Rotation of 90 degrees?
Definition
 (-y, x) Negate y then switch spots
Term
 Equivalent of -90 degrees?
Definition
 Rotation of 270 degrees
Term
 Glide Reflection?
Definition
 Line Reflection + Translation
Term
 What transformations changes isometries?
Definition
 Line Reflection and Glide Reflection
Term
 The sum of interior angles of a polygon is?
Definition
 Equal to 180(n-2). Divide that number by n (the number of sides) to get the number of degrees in one angle of a regular polygon.
Term
 The sum of exterior angles of a polygon?
Definition
 360. Divide 360 by n to get number of degrees in one exterior angle.
Term
 Formulas for lateral area and volume of a prism?
Definition
 Lateral area = perimeter of base x heightVolume = area of base x height
Term
 Formulas for lateral area and volume of a pyramid?
Definition
 Lateral area = 1/2 perimeter of base x slant heightVolume = 1/3 area of base x height
Term
 Formulas for lateral area and volume of a cylinder?
Definition
 Lateral area = circumference of base x heightVolume = area of base x height
Term
 Formulas for lateral area and volume of a cone?
Definition
 Lateral area = 1/2 circumference of base x slant height Volume = 1/3 area of base x height
Term
 Formulas for surface area and volume of asphere?
Definition
 Surface area = 4πr^2Volume = 4/3 πr^3
Term
 The length of a diagonal of a rectangular prism formula?
Definition
 [image]
Term
 If a sphere and a plane intersect, what is formed?
Definition
 A circle is formed. The largest capable circle that can be formed between two given spheres and planes is called the great circle.
Term
 Things that Were Not Covered By These Review Cards
Definition
 General Theorems, Circle Theorems, Plane Theorems
Term
 Reflection over the y-axis?
Definition
 (-x, y) Negate x
Term
 Reflection over the line y=x?
Definition
 (y, x) Switch order
Term
 Reflection over the line y=-x?
Definition
 (-y,-x) Negate both then switch
Term
 Rotation of 180 degrees?
Definition
 (-x, -y) Negate both
Term
 Rotation of 270 degrees?
Definition
 (y, -x) Negate x then switch
Term
 Equivalent of rotation of -180 degrees?
Definition
 Rotation of 180 degrees
Term
 Equivalent of rotation of -270 degrees?
Definition
 Rotation of 90 degrees
Term
 Equation of axis of symmetry?
Definition
 [image]
Term
 A condition is logically equivalent to its
Definition
 contrapositive
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