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Pretest Review

Pretest Review. Reviewing skills needed to succeed in Geometry. Solving Proportions. Cross Product Property!! ad = bc Example:. The Coordinate Plane:. Has 4 quadrants The origin is at (0,0) Coordinates are (x, y). X is horizontal coordinate, y is vertical coordinate.

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Pretest Review

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  1. Pretest Review Reviewing skills needed to succeed in Geometry.

  2. Solving Proportions • Cross Product Property!! ad = bc Example:

  3. The Coordinate Plane: • Has 4 quadrants • The origin is at (0,0) • Coordinates are (x, y). X is horizontal coordinate, y is vertical coordinate

  4. Linear Equations • 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:

  5. Forms of Equations of a Line • Slope Intercept: y = mx + b m= slope, b = y intercept • Standard Form: Ax + By = C • Point Slope Form: y – y1 = m (x – x1) m = slope, (x1, y1) = any point on the line (we will use this most often in this class)

  6. Writing Equations of a 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.

  7. The Graph of a Linear Equation • 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

  8. Solving a System of Equations with 2 variables: #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. • Then solve for x. • Use this value to find y.

  9. Perimeter, Area, Circumference, Volume • 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…

  10. Find the Surface Area and Volume:

  11. Triangle: Area = h b

  12. Circle: • Radius: r • Diameter: d =2r • Circumference: • C= d OR • C= 2 r • Area: A = r2 r d

  13. Circles: • If directions say leave in terms of , THEN LEAVE THE IN YOUR ANSWER!!!! Otherwise, use button on calculator.

  14. Vocabulary 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!!)

  15. Use the following image to answer the question. • Name a line.

  16. PLANES • 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

  17. Parallel Lines Parallel Lines:lines that do not intersect that are on the same plane (to name parallel lines, you can use the symbol ||)

  18. 1. Name 2 parallel segments. C D B A

  19. Parallel Planes F Planes that do not intersect Example: • Name a plane parallel to plane EGA. Answer: Plane FCB E C D H G B A

  20. Vocabulary • 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

  21. Examples: 2. 1. A B A B C Read “segment AB” or “segment BA” Read “Ray AB” or “Ray AC”. DO NOT write Ray BA or Ray CA. Must name endpoint first!!

  22. Triangles: • 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˚

  23. Angles: • Supplementary: 2 angles that add up to 180˚ • Complementary 2 angles that add up to 90˚

  24. Naming an Angle ANGLE ( ): Formed by 2 rays with the same endpoint To name an angle: To indicate angle measure: 3 possible ways: 1 (angle measure in degrees) Notice vertex is middle letter!

  25. Angles with a shared vertex: 1 2 • Must name using a numbered angle or using 3 points with vertex in the middle. • Cannot write “ angle B”.

  26. PYTHAGOREAN THEOREM • MUST be used on a right triangle • c is the hypotenuse, a and b are the legs of the right triangle a2 + b2 = c2

  27. The angles formed when a transversal intersects 2 lines depends on their position ALTERNATE INTERIOR ANGLES: Non-adjacent Lie on opposite sides of the transversal in between the 2 lines it intersects

  28. Same-Side Interior Angles (Co-interior) Lie on the same side of the transversal between the two lines

  29. Alternate Exterior Angles Lie outside the 2 lines on opposite sides of the transversal

  30. Same-Side Exterior Angles Lie outside the 2 lines on same side of transversal

  31. Corresponding Angles Lie on the same side of the transversal In corresponding positions

  32. Reducing Fractions: Look for common factors, and cancel them out to 1.

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