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Math 61 Plane Geometry

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  • Sample of what you should know before Math 61:
    1.   Solve: one eighth plus x equals 5 sixths x minus 2 thirds
    2. Find a simplified expression for the area and perimeter of the following shape.
    Rectangle with height x plus 1 and base 2 x plus 3
     3.  Factor:  24 a to the fourth plus 10 a cubed minus 4 a squared

     

  • Sample of what you will learn in Math 61:
    1. Find the measure of the numbered angles, given the lines m and n are parallel.
    Parallel horizontal lines labeled m on the top line and n on the bottom line with a third line that slopes upward from left to right cutting through m and n comma the top left angle formed by the third line cutting the m line is 131 degrees with the other angles labeled as 1 for the top right angle 2 for the bottom left angle and 3 for the bottom right angle comma the 4 angles formed by the third line cutting line n are labeled as 4 for the top left angle 5 for the top right angle 6 for the bottom left angle and 7 for the bottom right angle
      • Solution
        Angle 1 has measure 49 degrees since it is the supplement of 131 degrees.
        Angle 2 has measure 49 degrees since Angle 1 and Angle 2 are vertical angles.
        Angle 3 is 131 degrees since it is the supplement of Angle 2.
        Angle 4 is 131 degrees since Angle 3 and Angle 4 are alternate interior angles.
        Angle 5 is 49 degrees since it is the supplement of Angle 4.
        Angle 6 is 49 degrees since Angle 5 and Angle 6 are vertical angles.
        Angle 7 is 131 degrees since Angle 4 and Angle 7 are vertical angles.
    2. Solve for h
    A right triangle with the 90 degree angle at the top labeled at which point is labeled as capital B and the other two other points of the triangle labeled as capital A on the bottom left and capital C on the bottom right comma the side of the triangle connecting capital A and capital B is labeled as 9 comma the side of the triangle connecting capital C and capital B is labeled as 12 comma a dotted line is formed by dropping a line from capital B down to the base of the triangle which is the line connecting capital A and capital C forming a 90 degree angle with a c comma the point where the dotted line meets the line a c is labeled as capital d and the dotted line itself is labeled as lower case h
      • Solution
        First solve for side AC using the Pythagorean Theorem.
        9 squared plus 12 squared equals open parenthesis a c close parenthesis squared
        225 equals open parenthesis a c close parenthesis squared
        a c equals plus or minus 15
        Since side lengths must be positive we have a c equals 15
        Note the triangle ABC is similar to ADB. Similar triangles have corresponding sides in proportion.  Side AB of triangle ADB corresponds to side AC of triangle ABC and sides BC and CB correspond.  This leads to the proportion.
        9 fifteenths equals h over 12
        15 h equals 108
        so h equals 7 point 2