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February16 February20

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Problems and Solutions for the week of Feb 16 - Feb 20

Problems and Solutions for the week of Feb 16 - Feb 20

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    February16 February20 February16 February20 Presentation Transcript

    • Math Tutorial Questions For the week of February 16-20
    • Identifying Types of Lines and Planes Questions (3.1.1) – February 16, 2009
      • Use the diagram below to identify each of the following.
        • A pair of parallel segments
        • A pair of skew segments
        • A pair of perpendicular segments
        • A pair of parallel planes
      • Use the diagram to the right to identify each of the following.
        • A pair of parallel segments
        • A pair of skew segments
        • A pair of perpendicular segments
        • A pair of parallel planes
    • Identifying Types of Lines and Planes Solutions (3.1.1) – February 16, 2009
      • Use the diagram to the right to identify each of the following.
        • 3 example solutions are listed, there are other possibilities
        • A pair of parallel segments
        • AB & CD, CB & GF, EF & HG
        • A pair of skew segments
        • AE & GF, AB & DH, HG & BF
        • A pair of perpendicular segments
        • DH & HG, AD & DC, EF & FG
        • A pair of parallel planes
        • Plane DCG & Plane ABF, Plane ADH & Plane BCG, Plane ABC & Plane EFG
      • Use the diagram to the right to identify each of the following.
        • 3 example solutions are listed, there are other possibilities
        • A pair of parallel segments
        • KL & NM, LQ & MR, QR & PS
        • A pair of skew segments
        • KL & MR, LQ & PS, PQ & NS
        • A pair of perpendicular segments
        • KL & LQ, LQ & QR, KN & NS
        • A pair of parallel planes
        • Plane KLM & Plane PQR, Plane MLQ & Plane NKP, Plane NMR & Plane KLQ
    • Classifying Pairs of Angles
      • Use the diagram to the right to identify each of the following.
        • A pair alternate interior angles
        • A pair of corresponding angles
        • A pair of alternate exterior angles
        • A pair of same-side interior angles
      Questions (3.1.2) – February 17, 2009
      • Use the diagram to the right to identify each of the following.
        • A pair alternate interior angles
        • A pair of corresponding angles
        • A pair of alternate exterior angles
        • A pair of same-side interior angles
    • Classifying Pairs of Angles
      • Use the diagram to the right to identify each of the following.
      • 2 example solutions are listed, there are other possibilities
        • A pair alternate interior angles
        • Angles 3 & 5, Angles 4 & 6
        • A pair of corresponding angles
        • Angles 2 & 6, Angles 4 & 8
        • A pair of alternate exterior angles
        • Angles 2 & 8, Angles 1 & 7
        • A pair of same-side interior angles
        • Angles 4 & 5, Angles 3 & 6
      Solutions (3.1.2) – February 17, 2009
      • Use the diagram to the right to identify each of the following.
      • 1 example solution is listed, there are other possibilities
        • A pair alternate interior angles
        • Angle EHG & Angle HGK
        • A pair of corresponding angles
        • Angle EHG & Angle FGJ
        • A pair of alternate exterior angles
        • Angle IHE & Angle JGK
        • A pair of same-side interior angles
        • Angle EHG & Angle FGH
    • Angles Formed by Parallel Lines & Transversals Questions (3.2.3) – February 18, 2009
      • Use the diagram below to find each angle measure.
        • m ECF
        • m DCE
      • Find x and y in the diagram below.
    • Angles Formed by Parallel Lines & Transversals Solutions (3.2.3) – February 18, 2009
      • Use the diagram below to find each angle measure.
        • Corresponding angles are equal in measure.
        • Angle ECF & Angle EBG are corresponding.
        • Angle DCE & Angle ABE are corresponding.
        • m ECF
        • Angle ECF = Angle EBG (Substitute values in)
        • Angle ECF = 70º
        • m DCE
        • Angle DCE = Angle ABE (Substitute values in)
        • 5x = 4x + 22 (Subtract 4x from both sides)
        • x = 22
      • Find x and y in the diagram below.
      • Corresponding angles are equal in measure.
      • 5x + 5y = 60 (Subtract 5x from both sides)
      • 5y = 60 – 5x (Divide both sides by 5)
      • y = 12 – x
      • Alternate Interior angles are equal in measure.
      • 5x + 4y = 55 (Substitute y = 12 – x in for y)
      • 5x + 4(12 – x) = 55 (Multiply 4 through 12 – x)
      • 5x + 48 – 4x = 55 (Collect x terms together)
      • x + 48 = 55 (Subtract 48 from both sides)
      • x = 7
      y = 12 – x (Substitute 7 in for x) y = 12 – 7 (Subtract 12 and 7) y = 5
    • Slopes of Lines Questions (3.5.2) – February 19, 2009
      • Use the diagram below and the information above to determine the slope of each line.
        • AB
        • AC
        • AD
        • CD
      • Justin is driving from home to his college dormitory. At 4:00 P.M., he is 260 miles from home. At 7:00 P.M., he is 455 miles from home. Use the graph of the line that represents Justin’s distance from home at a given time. Find and interpret the slope of the line.
    • Slopes of Lines Solutions (3.5.2) – February 19, 2009
      • Use the diagram to the right to determine the slope of each line.
        • A(-2, 7), B(3, 7), C(4, 2), D(-2, 1)
        • AB
        • Line AB is horizontal, therefore the slope is 0.
        • AC
        • AD
        • Line AD is vertical, therefore the slope is UNDEFINED.
        • CD
      • Justin is driving from home to his college dormitory. At 4:00 P.M., he is 260 miles from home. At 7:00 P.M., he is 455 miles from home. Use the graph of the line that represents Justin’s distance from home at a given time. Find and interpret the slope of the line.
      The slope is 65 mi/hr, which means his average speed while driving home was at a rate of 65 miles per hour.
    • Using Slopes to Classify Pairs of Lines Questions (3.5.3) – February 20, 2009
      • Graph each pair of lines. Find their slopes and use them to determine whether the lines are parallel, perpendicular, or neither.
        • UV and XY for U(0, 2),
        • V(-1, -1), X(3, 1), Y(-3, 3)
        • GH and IJ for G(-3, -2),
        • H(1, 2), I(-2, 4), J(2, -4)
        • CD and EF for C(-1, -3),
        • D(1, 1), E(-1, 1), F(0, 3)
    • Using Slopes to Classify Pairs of Lines Solutions (3.5.3) – February 20, 2009
        • UV and XY
        • U(0, 2)
        • V(-1, -1)
        • X(3, 1)
        • Y(-3, 3)
        • GH and IJ
        • G(-3, -2)
        • H(1, 2)
        • I(-2, 4)
        • J(2, -4)
      • Graph each pair of lines. Find their slopes and use them to determine whether the lines are parallel, perpendicular, or neither.
        • CD and EF
        • C(-1, -3)
        • D(1, 1)
        • E(-1, 1)
        • F(0, 3)
      The slopes are 3 and -⅓, which multiply to equal -1, or are called opposite reciprocals of each other. Therefore the lines are perpendicular lines. The slopes are 1 and -2, which do not multiply to equal -1 and they are not the same slope. Therefore the lines are not perpendicular lines, and they are not parallel lines. The slopes are 2 and 2, which means they have the same slope. Therefore the lines are parallel lines.