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Final Exam Study Guide Period_______ Name_________________________________ Date__________________________________ Geometry: Triangles: Right triangle: A triangle whose largest angle is 90˚. Obtuse triangle: A triangle whose largest angle is more than 90˚. Acute triangle: A triangle whose largest angle is less than 90˚. (All angles are less than 90˚.) Equilateral triangle: A triangle with three congruent sides. (All sides equal.) Isosceles triangle: A triangle with two congruent sides. Scalene: A triangle with no congruent sides. The sum of the angles of a triangle is 180˚. Quadrilaterals: Parallelogram: A quadrilateral with 2 pair of parallel sides, opposite sides congruent. Rectangle: A quadrilateral with 2 pair of parallel sides, opposite sides congruent and four 90 degree angles. Square: A quadrilateral with 2 pair of parallel sides, all sides congruent and four 90 degree angles. Rhombus: A quadrilateral with four congruent sides, opposite sides parallel. Trapezoid: A quadrilateral with 1 pair of parallel sides. The sum of the angles of a quadrilateral is 360˚. Polygons: Pentagon: 5 sides Heptagon: 7 sides Nonagon: 9 sides Hexagon: 6 sides Octagon: 8 sides Decagon: 10 sides Interior angles: To find the sum of the interior angles of any polygon, use the formula (n-2)180˚, where n is the number of sides. Circles: Circle: A set of all points in a plane that are an equal distance from the center point. Radius: A segment from the center of the circle to any point on the circle. ( 2r = d) Diameter: A segment from one side of the circle to other, passing through the center. (1/2 d = r) Chord: A segment connecting any two points on the circle. Arc: Part of the circle. Semicircle: Half of the circle. Minor arc: An arc that is less than 180˚. Major arc: An arc that is more than 180˚, but less than 360˚. Central Angle: An angle whose vertex is at the center of the circle. There are 360˚ in a circle. Formulas: Area (triangle) = ½bh Area (parallelogram, rectangle, square) = bh or lw Area (trapezoid) = ½(b1 + b2)h Area (circle) = πr2 Circumference (circle) = πd or 2πr Surface Area of a prism: 2lw + 2lh + 2wh Surface Area of a cylinder: 2πr2 + 2πrh Volume of a prism: lwh Volume of cylinder: πr2h Cavallaro 16 Final Exam Study Guide Reference – Final Exam Review – Pg. 1 Final Exam Study Guide Period_______ Name_________________________________ Date__________________________________ Statistics: Mean: (Average) The sum of the data divided by the number of data items. Median: The middle number is a set of data that is written in order from least to greatest. If there is no middle number, find the mean of the two middle numbers. Mode: The data item that appears most often. There may be more than one mode. There is no mode if all data items occur the same number of times. Range: The difference between the greatest and the least values in a set of data. Outlier: A data item that is far apart from the rest of the data items. An outlier affects the mean more than the median or mode. Line Plot: A line plot uses a number line to display data. Each x represents a data item. Probability: Probability: The likelihood that an event will occur. Event: One or more results of an experiment. Compound Event: The combination of two or more single events. Certain Event: An event with a probability of 1. (It must happen.) Impossible Event: An event with a probability of 0. (It can not happen.) Theoretical Probability: The probability that is calculated by using the ratio: P = Number of favorable outcomes Number of possible outcomes Experimental Probability: The probability found by repeating an experiment, using the ratio: P= Number of times an event happens Number of times the experiment is done Complement: The complement for an event is all of the other possible events for a situation. The probability of an event plus the probability of its complement equals 1. Sample space: The set of all possible outcomes. Ex. The sample space for a coin is H, T. The sample space for a die is 1, 2, 3, 4, 5, 6. Counting Principle: The number of possible outcomes of a compound event equals the product of the number of outcomes of the individual event. Independent events: Two events are independent if the outcome of the first does not affect the outcome of a second. Probability of Independent Events: P(A and B) = P(A) x P(B) Dependent events: Two events are dependent if the outcome of the first event affects the outcome of the second event. Probability of Dependent Events: P(A, then B) = P(A) x P(B after A) Cavallaro 16 Final Exam Study Guide Reference – Final Exam Review – Pg. 2 Final Exam Study Guide Period_______ Name_________________________________ Date__________________________________ Ratio/Proportion/Percent Ratios: A comparison of two numbers. Ex. 3/5 Written three ways: 3 to 5 1) - as a fraction 2) - with the word “to” 3) - with a “ : “ 3:5 Rate: Comparison of two quantities. (Different units) 56 miles/ hour Unit Rate: A rate with a denominator of 1. Constant of Proportionality: Another name for the unit rate. Proportion: A statement that two ratios are equal. To determine if two ratios are a proportion: 1) Cross multiply. If the cross products are equal, it is a proportion. If the cross products are not equal, it is not a proportion. To find the missing value in a proportion: 1) Cross multiply the two numbers. 2) Divide the cross product by the remaining number. 3) The quotient is the answer. Be sure to label. Ex. x = 7 4 • 7 = 9 • x 4 9 28 = 9x 9 9 3.11… = x x = 3.11… Percent: Per one-hundred. PERCENTS ARE ALWAYS OVER 100 To solve any percent question use the equation: % = is 100 of To change a percent to a fraction: drop the % and place it over 100. REDUCE To change a percent to a decimal: move the decimal two places to the left. (Divide by 100) To change from a decimal to a percent: Move the decimal two places to the right. (Mult. by 100) To change from a decimal to a fraction: place the decimal (with-out the point) over the correct power of ten. To change from a fraction to a percent. Use the numerator as the percent if it is over 100 or set up a proportion to find its equivalent fraction with a denominator of 100. To change from a fraction to a decimal: Divide the numerator by the denominator. Fraction Decimal Percent 1/2 .5 50% 7/8 .875 87.5% Cavallaro 16 Final Exam Study Guide Reference – Final Exam Review – Pg. 3 Final Exam Study Guide Period_______ Name_________________________________ Date__________________________________ Angle Relationships: Adjacent angles: Angles that have a common side and a common vertex. There is no degree measurement for adjacent angles. Complementary angles: Two angles whose sum is 90°. The angles do not have to be adjacent. 1 and 2 are complementary angles. Figure A. Supplementary angles: Two angles whose sum is 180°. The angles do not have to be adjacent. 3 and 4 are supplementary angles. Figure B. 1 3 2 4 Figure B Figure A Vertical angles: Opposite angles. Vertical angles are formed by the intersection of two straight lines. Vertical angles must share a vertex, but do not share a side. 1 and 3 are vertical angels. 2 and 4 are also vertical angles. Vertical angles have equal measures. 1 4 3 l1 2 l2 Transversal: The line that intersects two lines at separate places. Corresponding angles: Angles that hold the same position with respect to the transversal. 1 and 5 are corresponding angles. They are both above the lines and to the left of the transversal. 2 and 6, 3 and 7, and 4 and 8 are also corresponding angles. Corresponding angles have equal measures. Alternate interior angles: Angles that are between the lines and on opposite sides of the transversal. 3 and 5 are alternate interior angles. 4 and 6 are also alternate interior angles. Alternate interior angles have the same measure. Alternate exterior angles: Angles that are on the outsides of the lines and on opposite sides of the transversal. 1 and 7 are alternate exterior angles. 2 and 8 are also alternate exterior angles. Alternate exterior angles have the same measure. t 1 2 l1 4 3 5 8 6 l2 7 Given that l1 and l2 are parallel. Cavallaro 16 Final Exam Study Guide Reference – Final Exam Review – Pg. 4