GRE

If P(E) is the probability that an event WILL occur, what is the probability that an event will NOT occur?

1-P(E)

What is the exterior angle of a triangle?

1. If there are interior angles given and you are asked for the remaining exterior angle then you add the interior angles together. 2. If there are three exterior angles being added they add up to 360 degrees.

To find the volume or surface area of a cylinder, you'll need two pieces of information:

1. The height of the cylinder 2. The Radius of the base Volume of a cylinder= (Area of the base)(height)= pie x r(squared) x height (h) Lateral surface area of a cylinder= (circumference of base)(height)= 2pie rh Total surface area of a cylinder = Areas of circular ends + lateral surface area = 2pie rsquared + 2pie rh

The area of a triangle

1/2 (base)(height) Example: Length =4 Height/altitude=3 Area= 1/2bh =bh/2 =4x3/2 =6 Since the lengths of the base and altitude were not given in specific units it = 6 square units

What is the sum of the interior angles of any triangle?

180 degrees.

What is the sum of the measures of the angles on one side of a straight line?

180 degrees.

What is the sum of the measures of the angles around a point?

360 degrees.

Polygons

A closed figure whose sides are straight line segments. Families or classes of polygons are named according to their number of sides. Triangle= 3 sides Quadrilateral = 4 sides Pentagon = 5 sides Hexagon= 6 sides Triangles and Quadrilaterals are by far the most important polygons on the GRE. Other polygons appear only occasionally.

Combination

A combination question asks you how many unordered subgroups can be formed from a larger group. -Some cases are quick and easy as in AB, AC, BC as possible combinations. -Some require the combination formula: n!/k!(n-k)! n= the number of items in the group as a whole k=the number of items in each subgroup formed != means factorial Ex. 5!= 5x4x3x2x1 =120

Plane

A flat surface that extends indefinitely in any direction

Angle Bisectors

A line or line segment bisects an angle if it splits the angle into two smaller, equal angles. Important to remember both sides are then equal to each other!

Diagonal of a polygon

A line segment connecting any two nonadjacent vertices.

Edge

A line segment that connects adjacent faces of a solid. The sides of a hexagon ABCDEF are also edges on the face of something.

Radius

A line segment that connects the center of the circle with any point on the circle (plural Radii). The radius of a circle is one-half the length of the diameter. In circle 0 above, OA. OB, OC are radii.

Diameter

A line segment that connects two points on the circle and passes through the center of the circle. AB is a diameter of circle 0.

Angles around parallel lines intersected by a transversal

A line that intersects two parallel lines is called a transversal. Each of the parallel lines intersects the third line at the same angle. Anything that is parallel or opposite angles are equal *When two or more parallel lines are cut by a transversal, all acute angles formed are equal, all obtuse angles formed are equal, and any acute angle formed is supplementary to any obtuse angle formed.

Lists

A list is like a finite set except that the order of the elements matters and that duplicate members can be included. So 1,2,3 and 3,2,1 are different lists and 1,2,3,2 is a valid list. *Order MATTERS in lists -elements can be uniquely identified by their position such as the 'first element' or the 'fifth element' *Lists are not enclosed within brackets.

Vertex of a polygon

A point where two sides intersect (plural: vertices). Polygons are named by assigning each vertex a letter and listing them in order.

Circumscribed Figures

A polygon is circumscribed about a circle if all the sides of the polygon are tangent to the circle.

Inscribed figures

A polygon is inscribed in a circle if all the vertices of the polygon lie on the circle.

Regular Polygon

A polygon with sides of equal length and interior angles of equal length and interior angles or equal measure. Small slash marks can provide important information in diagrams of polygons. Sides with the same number of slash marks are equal in length, while angles with the same number of slash marks through circular arcs have the same measure.

Triangle

A polygon with three straight sides and three interior angles

Quadrilaterals

A quadrilateral is a four sided polygon. Regardless of a quadrilateral's shape, the four interior angles sum to 360. Type I: Parallelogram: quadrilateral with two pairs of parallel sides. Opposite sides are equal in length; opposite angles are equal in measure. Angles that are not opposite are supplementary to each other. Type II: Rectangle- A type of parallelogram with four right angles. Opposite sides are equal and diagonals are equal. Type III: A square is a rectangle with equal sides.

Square

A rectangle with equal sides which is a type of quadrilateral.

When a triangle is inscribed in a semicircle in such a way that one side of the triangle coincides with the diameter of the semicircle, then what is the triangle?

A right triangle ex. pg 329 What is the diameter of semicircle 0? AC is a diameter of semicircle 0 because it passes through center point O. So triangle ABC fits the description given above of a right triangle. Moreover, triangle ABC is a special 5:12:13 right triangle with a hypotenuse of 13. Therefore, the length of diameter AC is 13.

Uniform Solid

A solid that could be cut into congruent cross sections (parallel slices of equal size and shape) along a given axis. Solids you see on the GRE will almost certainly be uniform solids.

Rectangular Solid

A solid with six rectangular faces. All edges meet at right angles. Examples of rectangular solids are cereal boxes, bricks, etc.

Cube

A special rectangular solid in which all edges are of equal length. All faces are squares. Sugar cubes and dice without rounded corners are examples of cubes.

Solid

A three-dimensional figure. The dimensions are usually called length, width, and height (l,w and h). There are only two types of solids that appear with any frequency on the GRE 1. Rectangular Solids (including cubes) 2. Cylinders

Equilateral triangle

A triangle whose three sides are all equal in length and whose three interior angles each measure 60 degrees. The altitude or height of a triangle is the perpendicular distance from a vertex to the side opposite the vertex. The altitude may fall inside or outside the triangle, or it may coincide with one of the sides.

Right Triangle

A triangle with one interior angle of 90 degrees ( a right angle)

Isosceles Triangle

A triangle with two equal sides which are opposite two equal angles.

Cylinder

A uniform solid whose horizontal cross section is a circle ex: a soup can or a pipe that is closed at both ends. A cylinder's measurements are generally given in terms of its radius (r- along x axis) or its height (h-along the y axis).

How do you find the perimeter of a polygon?

Add the lengths of its sides. The properties of rectangles and squares lead to simple formulas that may speed up your calculations. Because the opposite sides are equal, the perimeter of a rectangle is twice the sum of the length and the width Perimeter = 2(length + Width) Ex: The perimeter of a 5 by 2 rectangle is 2(5+2)=14 Perimeter of a SQUARE: is equal to the sum of the lengths of the 4 sides. Because all 4 sides are the same length, perimeter = 4 (side). If the length of one side of a square is 3, the perimeter is 4x3=12

Central Angle

An angle formed by two Radii. The total of a degree measure of a circle is 360 degrees.

Volume of a rectangular solid

Area of the base x height = (length x width) (Height)lwh

What do you do in situations where there is an or instead of an 'and'?

As long as the two groups are mutually exclusive, ADD instead of multiplying.

How do you figure out the sum of the interior angles of a polygon?

By dividing the polygon into triangles. Draw diagonals from any vertex to all the nonadjacent vertices. Then multiply the number of triangles by 180 degrees to get the sum of the interior angles of the polygon. This works because the sum of the interior angles of any triangle is always 180 degrees.

A and B are overlapping sets. If IAI has 7 elements, IBI has 5 and IA∩BI has 3 elements, how many elements are in IAUBI?

Counting Method and Probability Practice Set Question. IAUBI= IAI + IBI - IA∩BI IAUBI= 7+5-3=9 ∩= Intersection of two sets (has to be in both:overlap).

What is the probability of the results of 4 independent coin flips being exactly 1 head and 3 tails?

Counting Methods and Probability Practice Set Question. Total Outcomes: 2 to the 4th power=16. There are 4 desired outcomes. 4/16=1/4

A bag contains only 4 orange marbles and 2 blue marbles. Latisha wants to get a blue marble from the bag, but she cannot see what color marble she draws until she takes it out of the bag. Latisha will stop drawing marbles as soon as she gets a blue one. If Latisha does not draw a blue marble in 3 attempts, she stops. What is the probability that she will draw a blue marble?

Counting Methods and Probability Practice Set Questions. Most efficient method is to focus on the probability she will NOT draw a blue marble in 3 attempts and subtract that from 1 to get the probability that she will. 4/6=2/3rds chance she won't draw a blue. For the second there will only be 5 remaining, 3 of which won't be blue. 3/5 on second chance. Third time: 2/4 left=1/2. In order not to draw any blue marbles, Latisha will have to be unsuccessful on the first AND second AND third attempts, so the probability of that happening is 2/3 x 3/5 x 1/2 = 1/5. Therefore, the probability that she will be successful is 1-1/5=4/5

Lee likes both country and pop music. Her playlist has a total of 60 songs that are categorized as pop, country, or rock. If a song is listed as both pop and country, it is considered crossover music. If 24 of Lee's songs are classified as rock music only, 30 are pop, and 18 are country, how many are crossover?

Counting Methods and Probability Practice Set Questions. Use the Formula for Overlapping sets: Total= Group A + Group B - Both + Neither *Since the question defines crossover as country and pop, the rock songs can be considered neither. Plug the given values into the equation 60=30+18- Crossover + 24. Add crossover to both sides of the equation and subtract 60 from both sides to get: Crossover = 30+18+24-60=12

A bag contains only red and blue plastic chips. There were 10 chips in the bag and 1 blue chip was removed. The probability of drawing a blue chip was then 1/3. How many red chips were in the bag?

Counting Methods and Probability Practice Set Questions. After 1 blue chip was removed, there were 9 chips left. If the probability of drawing another blue chip from those remaining 9 was then 1/3, there must have been 1/3 x 9 =3 blue chips, and 9-3=6 red chips remaining. Since no red chips were drawn, the original number of red chips must also have been 6.

How many ways are there to fill a candelabra with 4 candle holders from a box of 6 distinctly colored candles?

Counting Methods and Probability Review Order DOES matter here because they are distinctly colored. There are 6 possible candles for the first slot, 5 for the second, 4 for the third, and 3 for the 4th. To find the total number of possibilities, multiply each of the possibilities for the four slots together 6x5x4x3=360

In a recent election for two different positions elected by the same voters, candidates A and B were chosen by a majority of the voters. Two-thirds of the 60% of voters who chose candidate A also voted for Candidate B. The percentage of voters who did not vote for either candidate must have been less than __________?

Counting Methods and Probability Review Overlapping Sets Question Step1: Set up a table to organize the information and derive the values needed Step2: Horizontal Row: For A, Not for A, and Total Step3: Vertical Columns: For b, Not for B, and Total Step 4: Total for categories must be 100% Step 5: Chosen by a majority means >50% Step6: < 30% must be the answer.

Pablo is allowed to choose 1 of 3 different fruit beverages and 2 of 4 different healthy grain bars for his afternoon snack. How many different combinations does he have from which to choose?

Counting Methods and Probability Review The number of options for the beverage is 3. *To calculate the number of options for grain bars, use the combinations formula, because the order in which pablo selects the 2 grain bars doesn't matter. 4C2= 4!/2!(4-2)! = 4x3x2x1/2x1x2x1=6 Since Pablo gets to choose a beverage and two grain bars, and for each of the 3 beverages he can choose from 6 different options of grain bars, multiply the two numbers of choices: 3x6=18

What is the probability that one roll of a fair six-sided die will result in an even number?

Counting Methods and Probability Review. A roll of a 2 or 4 or 6 would meet the criterion in the question. These are mutually exclusive outcomes, so add their probabilities: 1/6 + 1/6 +1/6 = 3/6 =1/2

A certain platoon is made up of 3 squads, each of which has 4 soldiers. When the platoon lines up to enter the mess hall, the squads are allowed to be in any order but the soldiers must line up within their squads according to certain rules. The soldiers in the first squad can line up any way they want as long as they stay with their squad. The squad leader of the second squad insists that the soldiers in that squad be in one particular order. The third squad leader wants the soldiers in that squad to line up in order from either tallest to shortest or shortest to tallest. How many different ways can the platoon line up?

Counting Methods and Probability Review. Groups of Groups Pattern. Step 1: Consider how many ways the groups (squads) can be arranged. Since there are 3 distinct squads, taht is 3! = 3x2x1 =6 different ways. For the squad that is permitted to choose any order they wish, there are 4! = 4x3x2x1 =24 different ways they can line up. *The squad that lines up by height can only have 2 variations and the remaining squad only has one way to line up within the squad. Therefore, the total number of ways that the platoon can line up is 6x24x2x1=288

Paula has 10 books that she would like to read on vacation, but she only has space for 3 books in her suitcase. How many different groups of 3 books can paula pack?

Counting Methods and Probability Review. Since the books are just being put in the suitcase, order doesn't matter, and the combinations formula can be used. Combination Formula: 10C3= 10!/3!(10-3)! =10x9x8x7!/3!7! =10x9x8/3x2 =720/6 =120

A six-sided die used for a board game has the letter R on 3 sides, S on 2 sides, and T on the remaining side. What is the probability of rolling an R, an S, and a T on 3 rolls of the die in any order?

Counting Methods and Probability Review. The desired outcome is R-S-T in any order. The probability of rolling an R (PR) on any roll is 3/6=1/2 Similarly PS= 2/6=1/3 PR= 1/6 Thus the probability of rolling one of each is 1/2x1/3x1/6= 1/36 *There are 3!=6 different orders in which R-S-T can be rolled, so the total probability of rolling R-S-T in any order is 6x1/36=1/6

What is the probability of rolling a six on two consecutive rolls of a fair six-sided die?

Counting Methods and Probability Review. There are 6 equally likely outcomes for one roll of a fair die. One of these outcomes is 6, so the probability of rolling a 6 is 1/6. The question asks for the probability of rolling a 6 on the first roll AND the probability of rolling a 6 on the second roll. These events are independent so multiply the two probabilities: 1/6 x 1/6 = 1/36

How many different-appearing arrangements can be created using all the letters AAABBC?

Counting Methods and Probability Review. This Question represents a pattern of a counting problem with certain conditions or restrictions added. *There are 6 ways to arrange 6 different items however many will look identical *The number of different-appearing arrangements is 6!/3!(2!) This simplifies to 6x5x4x3x2x1/3x2x1x2x1 which equals 5x4x3/1 which = 60

Events A and B are independent, but not mutually exclusive. The probability that event A occurs is 0.5 and the probability that at least one of the events A or B occurs is 0.8. What is the probability that event B occurs?

Counting Methods and Probability Review. Use the formula for two independent events to calculate the probability that event B occurs. Designate the probability that A occurs as P subA, that B occurs as P sub B, and the probability that at least one occurs as P subAorB. From the question, P subA= 0.5 P sub AorB= 0.8. The formula for P sub AorB = PA + PB - PAandB *Since the events are independent, PAandB= PAxPB. Thus the formula can be written as PAorB= PA +PB- (PAxPB). Plug in the known values to get: 0.8=0.5+PB-(0.5xPB) -0.8-.05=PB-0.5PB -0.3=0.5PB -0.6=PB PB= Probability of B

How do you find the shortest distance from a point to a line?

Draw a line segment from the point to the line such that the line segment is perpendicular to the line. Then measure the length of that segment.

What is the sum of the interior angles of a pentagon?

Draw a pentagon ( a five sided polygon) and divided it into triangles. No matter how you've drawn the pentagon, you'll be able to form three triangles. Therefore, the sum of the interior angles of a pentagon is 3x180 degrees = 540 degrees.

How do you find the length of a line segment parallel to one of the axes?

Find the difference between the endpoint coordinates that do change. Treat the line segment as the hypotenuse of a right triangle. Simply draw the legs of the triangle parallel to the two axes. The length of each leg wil be the difference between the x or y coordinates of its endpoints. Once you've found the lengths of the legs, you can use the pythagorean theorem to find the length of the hypotenuse (the original line segment). Hypotenuse squared = line one squared + line two squared

When are two lines parallel?

If they lie on the same plane and never intersect regardless of how far they are extended. L1 II L2 is how you signify parallel lines.

Intersection vs Unions

Intersection: of two sets is a set that consists of all the elements that are contained in both sets (overlap) A∩B Union: of two sets is the set of all the elements that are elements of either or both sets and is written as A U B. *If sets have no common elements, they are referred to as mutually exclusive and their intersection is an empty set. *Use a Venn Diagram.

Area formulas always involve what?

Multiplication and results are in squares. Area of a Rectangle: Length x Width Area of a Square: side squared (don't multiple. this would give you the perimeter) Parallelogram: Designate one side as the base (b) then draw a line segment from one of the vertices opposite the base down to the base to that it intersects at a right angle. That line segment = height (h). To find the area of the parallelogram, multiply the length of the base by the length of the height. Area of Parallelogram = (base)(height) or A =bh *remember in a parallelogram if you know two adjacent sides, you know all of them. And if you know two adjacent angles, you know all of them. *In a rectangle, if you know two adjacent sides, you know the area *in a square, if you're given virtually any measurement (area, length of a side, length of a diagonal) you can figure out the other measurements.

How do you calculate the probability of two or more independent events occurring?

Multiply the probabilities of the individual events

Permutation

Permutation is multiple arrangements. Within a group of 3 items (ABC) there are six permutations. -Permutations differ from combinations in that permutations are ordered. Ex: "How many ways/arrangements/orders/schedules are possible?" This will indicate a permutation problem.

How do you solve multiple figures geometry questions?

Revisualize the side of a rectangle as the hypotenuse of a neighboring right triangle or as the diameter of a circumscribed circle. Keep looking for the relationship between the different figures until you find one that leads you to the correct answer. Type I: Diagram of a geometrical figure that has been broken up into different, irregularly shaped areas, often with one region shaded. You'll usually be asked to find the area of the shaded (or unshaded) portion of the diagram. Your best bet will be to take one of the following two approaches 1. Break the area into smaller pieces whose separate areas you can find. Add those areas together. 2. Find the area of the whole figure; find the area of the region(s) that you're not looking for; subtract the latter from the former. Ex. Pg. 328 Rectangle ABCD above has an area of 72 and is composed of 8 equal squares. What is the area of the shaded region? The first thing you have to realize is that, for the 8 equal squares to form a total area of 72, each square must have an area of 82/8=9. Since the area of a square equals the square of a length of a side, each side of a square in the diagram must have a length of the square root of 9=3 Approach 1: Break up the shaded area. Approach 2: Get the total unshaded area. Then subtract the total unshaded area from the total area of the rectangle where the unshaded areas are.

Sets

Sets are groups of values that have some common property *items are called elements or members -If all the elements in a set can be counted that set is finite -If the elements in a set are limitless that set is infinite. -The set with no elements is called an empty set, which is represented by the symbol O with a line through it. -A set with any members is nonempty -If all the elements of set A are among the elements of set B, then A is a subset of B. By definition, the empty set is a subset of all sets. -Elements in sets are unique and cannot be repeated (in lists they can). -Order does not matter in sets. (it does in lists).

Equation of lines

Straight lines are described by linear equations: y=mx + b m= slope (y/x) Rise over run b= the point where the line intercepts the y-axis *Lines parallel to the x axis have a slope of zero and therefore have an equation of y=b *Lines that are parallel to the y-axis have the equation x=a where a is the x-intercept of that line.

Surface area of a rectangular solid

Sum of areas of faces = 2lw + 2lh + 2hw *Since a cube is a rectangular solid for which l=w=h, the formula for its volume can be stated in terms of any edge: Volume of a cube= lwh= (edge)(edge)(edge)=e to the third power Surface area of a cube= sum of areas of faces = 6e to the second power

Base

The bottom face of a solid as oriented in any given diagram

Perimeter

The distance around a polygon The Sum of the lengths of its sides.

Distance on the coordinate plane

The distance between two points is equal to the length of the straight-line segment that has those two points as endpoints.

If the lengths of two sides of a triangle are unequal, where is the greater angle?

The greater angle lies opposite the longer side and vice versa. Since the two legs of an isosceles triangle have the same length, the two angles opposite the legs must have the same measure.

What does probability measure?

The likelihood that an event will occur. Represented as a fraction, decimal or percent. Expressed as a number between 0 and 1 inclusive with a probability of 0 meaning 'no chance' and a probability of 1 meaning 'guaranteed to happen'. The higher than the probability, the greater the chance that an event will occur. An event can include more than one outcome. Many GRE probability questions are based on random experiments with a defined number of possible outcomes such as drawing a random card from a full deck. If all the possible outcomes of the experiment are equally likely to occur, you can use this formula to calculate probability: Probability = the number of desired outcomes/number of possible outcomes.

Coordinate Geometry

The locations of points in a plane are indicated by ordered pairs of real numbers.

Hypotenuse

The longest side of a right triangle. The hypotenuse is always opposite the right angle.

What do you do if asked to find the number of possible subgroups when choosing one item from a set?

The number of possible subgroups will always equal the number of items in the set.

Coordinates

The numbers that designate distance from an axis in coordinate geometry. The first number is the x-coordinate; the second is the y-coordinate. In the ordered pair (8,7), 8 is the x coordinate and 7 is the y-coordinate.

Lateral surface of a cylinder

The pipe surface, as opposed to the circular 'ends'. The lateral surface of a cylinder is unlike most other surfaces of solids that you'll see on the GRE 1. It does not lie in a plane 2. It forms a closed loop. Think of it as the label around a soup can. If you could remove it from the can in one piece, you would have an open tube. If you then cut the label and unrolled it, it would form a rectangle with a length equal to the circumference of the circular base of the can and a height equal to that of the can.

Origin

The point where the x and y axes intersect. Its coordinates are (0,0)

How do you interpret the probability of A or B?

The probability of A or B or both and the formula for calculating this is similar to the inclusion-exclusion principle for sets P(A or B) = P(A) + P(B) - P (A and B) *Probability of one OR another event occuring

Circle

The set of all points in a plan at the same distance from a certain point. This point is called the center of the circle. A circle is labeled by its center point; circle ) means the circle with center point O.

what does the area of a square equal?

The square of the length of a side.

Sides and Angles

The sum of the lengths of any two sides of a triangle is great than the length of the third side.

Face

The surface of a solid that lies in a particular plane. Hexagon ABCDEF is one face of the solid. (like the face of something).

Legs

The two equal sides of an isosceles triangle or the two shorter sides of a right triangle (the one forming the right angle). Note: The third, unequal side of an isosceles triangle is called the base.

How do you find the perimeter of a triangle?

There is no special formula. Just sum the lengths of the sides. Ex. If b= 2a c= 2/b find perimeter of a Perimeter = a + b + c = a + 2a + 2a/2 =3a + 2a/2 = 3a + a =4a *Incidentally, this is really an isosceles triangle, since c= b/2 = 2a/2 =a

Complementary Angle

Two angles that measures sum to 90 degrees.

Adjacent and Vertical Angles

Two intersecting lines form four angles. The angles that are adjacent (next) to each other are supplementary because they lie along a straight line. The two angles that are not adjacent to each other are opposite or vertical. Opposite angles are equal in measure because each of them is supplementary to the same adjacent angle.

Perpendicular

Two lines that intersect at a 90 degree angle (a right angle).

Ordered pair

Two numbers or quantities separated by a comma and enclosed in parentheses. An example would be (8,7). All the ordered pairs that you'll see in GRE coordinate geometry problems will be in the form (x,y), where the first quantity, x, tells you how far the point is to the left or right of the y-axis. The second quantity, y, tells you how far above or below the x-axis.

How do you measure an angle?

Using degrees. Angles are named according to their vertices. Sometimes when two or more angles share a common vertex, an angle is named according to three points 1. A point along one of the lines or line segments that form an angle 2. The vertex point 3. Another point along the other line or line segment. A diagram will sometimes show a letter inside the angle and this letter may be used to name the angle.

What can you find if you have one side of an isosceles right triangle and 30/60/90 degree triangles?

You can find everything

What can you find if you have two sides of a right triangle?

You can find the third side and you can find the area.

If the coordinates of point A are (3,4) and the coordinates of point B are (6,8) what is the distance between points A and B?

You don't have to draw the diagram unless you need to see it visually. Plot points A and B and draw a line segment AB. The length of AB is the distance between the two points. Step 2: Now draw a right triangle with AB as its hypotenuse. The missing vertex will be the intersection of a line segment drawn through point a parallel to the x-axis and a line segment drawn through point B parallel to the Y-axis. Label the point of intersection C. Since the x and y axes are perpendicular to each other, AC and BC will also be perpendicular to each other. *Point C will also have the same x cooridnate as point B and the same Y coordinate as point A. That means that point C has coordinates (6,4). *To use the Pythagorean Theorem, you'll need the lengths of AC and BC. The distance between points A and C is simply the difference between their x coordinates While the distance between points B and C is the difference between their y coordinates. So AC= 6-3=3 and BC= 8-4=4. If you recognize these as the legs of a 3:4:5 right triangle, you'll know immediately that the distance between points A and B must be 5. Otherwise, you'll have to use the pythagorean theorem to come to the same conclusion.

How do you solve slope intercept questions where they ask 'which points lie on the line going through two points?

You plug in the answers to slope-intercept form y=mx+b Then you plug in answer choices to the Y and X positions to see which one makes the equation true. Try to pick choices that will avoid fractions first.

Inclusion-Exclusion Principle

a basic counting principle of sets. Venn diagram shaded areas represent intersection. To find the number of elements in the union of two sets use the formula: IA U BI = IAI + IBI - IA∩BI This formula adjusts for the double counting of elements that are in both sets.

Rectangle

a parallelogram with four right angles. Opposite sides are equal and diagonals are equal. This is a type of quadrilateral

Obtuse angle

measures between 90 and 180 degrees

Acute Angle

measures less than 90 degrees

Two angles are __________ to each other if their measures sum to 180 degrees?

supplementary

What is the longest side of a right triangle?

the hypotenuse. This is the side opposite the 90 degree angle on a triangle.

Vertex

the point at which two lines or line segments intersect to form an angle.

Supplementary Angle

two angles whose measures sum to 180 degrees.