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February16 February20

on Feb 12, 2009

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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 February20Presentation 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
• 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
• 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.