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Reviewing skills needed to succeed in Geometry. • Cross Product Property!! a c b d Example: 3 2 x 5 3 ad = bc Answer : 3(3) 2( x 5) 9 2 x 10 19 2 x 19 x 2 • Has 4 quadrants • The origin is at (0,0) • Coordinates are (x, y). X is horizontal coordinate, y is vertical coordinate • • • • • Parallel lines = same slope Perpendicular lines = opposite, reciprocal slope Vertical lines = undefined slope (Equation is x = a ) Horizontal lines = slope of 0 ( Equation is y = b) To find the slope between 2 points on a line: y2 y1 m x2 x1 • Slope Intercept: y = mx + b m= slope, b = y intercept (we will use this most often in this class) • Standard Form: Ax + By = C • Point Slope Form: y – y1 = m (x – x1) m = slope, (x1, y1) = any point on the line • Need a point on the line and the slope of the line • If given 2 points, find the slope first, then use either point • Use algebra to move back and forth between forms of a line Example: Write the equation in slope intercept form of the line that passes through point (-2, 1) and has a slope of 3. Answer : y mx b 1 (3)(2) b 1 6 b b7 Equation : y 3 x 7 • • • • X – intercept : y coordinate= 0 Y- intercept : x coordinate = 0 Can graph using intercepts or in slope-intercept form To graph in slope-intercept: graph the y-intercept, use slope to graph other points • Graph the equation: y=2x+1 y intercept: 1 Slope: 2 #20 on packet: • Since y is isolated in equation 1, we can use the substitution method. • Substitute 3x-5 from the first equation in for y in the second. Answer : • Then solve for x. y 3x 5 • Use this value to find y. 4 x 3 y 35 4 x 3(3 x 5) 35 4 x 9 x 15 35 5 x 15 35 5 x 50 x 10 y 3(10) 5 25 Answer (10,25) • Perimeter: The sum of the lengths of the sides of a polygon (called circumference for circles) • Units of measurement: in, yds, ft, miles, meters, etc.. • Area: The number of square units a polygon encloses • Units of measurement: in2, cm2, mi2, etc… • Volume: How much space an object takes up • Units of measurement: in3, cm3, mi3, etc… Answer : Volume l w h 12(6)(5) 360un 2 SurfaceArea 2lw 2 wh 2lh 2(12)(6) 2(6)(5) 2(12)(5) 144 60 120 324un 2 1 Area = bh 2 h b • Radius: r • Diameter: d =2r • Circumference: • C= d OR • C= 2 r • Area: A = r2 r d • If directions say leave in terms of , THEN LEAVE THE IN YOUR ANSWER!!!! Otherwise, use button on calculator. Line: A series of points that extends in 2 opposite directions without end Can name a line by any two points on the line with a line above it, or by a single lower case letter. (Please note: In Geometry, it is important to use the correct notations!!) 1. Name a line. Examples : AB, EF , CB, etc. • A flat surface that has no thickness • Contains many lines • Extends w/o end in the direction of all its lines • Named by a single capital letter OR by AT LEAST 3 POINTS NOT ON THE SAME LINE Parallel Lines: lines that do not intersect that are on the same plane (to name parallel lines, you can use the symbol ||) 1. Name 2 parallel segments. AD || BC C D B A Planes that do not intersect F E C D Example: 1. Name a plane parallel to plane EGA. Answer: Plane FCB H G A B • Segment: part of the line consisting of 2 endpoints and all the points between them • How you name a segment: Use the 2 endpoints with a straight line above. • Ray: part of a line consisting of one endpoint and all the points of the line on one side of the endpoint • How you name a ray: Endpoint must be first, then any other point on the ray; write an arrow pointing to the right above 1. A B 2. A B AB or AB or BA AC Read “segment AB” or “segment BA” Read “Ray AB” or “Ray AC”. DO NOT write Ray BA or Ray CA. Must name endpoint first!! C • Classify by sides: Scalene, Isosceles, or Equilateral • Classify by angles: Acute, Obtuse, Straight or Right • All angles add up to 180˚ • All straight angles form a line, therefore measure 180˚ • Supplementary: 2 angles that add up to 180˚ • Complementary 2 angles that add up to 90˚ ANGLE ( ): Formed by 2 rays with the same endpoint 1 To name an angle: 3 possible ways: E 1 FED, DEF Notice vertex is middle letter! To indicate angle measure: mE (angle measure in degrees) 1 2 • Must name using a numbered angle or using 3 points with vertex in the middle. • Cannot write “ angle B”. 1 CBA 2 DBA MUST be used on a right triangle c is the hypotenuse, a and b are the legs of the right triangle 2 a + 2 b = 2 c ALTERNATE INTERIOR ANGLES: • Non-adjacent • Lie on opposite sides of the transversal in between the 2 lines it intersects C , B and A, D • Lie on the same side of the transversal between the two lines • Lie outside the 2 lines on opposite sides of the transversal • Lie outside the 2 lines on same side of transversal 1, 8 and 2, 7 • Lie on the same side of the transversal • In corresponding positions o, s or p, t or n, r or m, q 12 3 4 4 15 3 5 5 Look for common factors, and cancel them out to 1.