NOVEMBER 7, 2016
UNIT 3: LINEAR FUNCTIONS
SECTION 6.2:
SLOPES OF PARALLEL AND
PERPENDICULAR LINES
M. MALTBY INGERSOLL
NUMBERS, RELATIONS AND FUNCTIONS 10
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WHAT'S THE POINT OF TODAY'S LESSON?
We will continue working on the NRF 10 Specific Curriculum Outcome (SCO) "Relations and Functions 3" OR "RF3" which states:
"Demonstrate an understanding of slope with respect to rise and run, line segments and lines, rate of change, parallel lines and perpendicular lines."
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What does THAT mean???
SCO RF3 means that we will:
* determine the SLOPE, "m" (steepness) of a line by measuring or calculating the RISE (change in y) and RUN (change in x)
* classify lines in a given set as having POSITIVE slopes (the lines ASCEND from left to right) or NEGATIVE slopes (the lines DESCEND from left to right)
* explain the meaning of the slope of a HORIZONTAL line (y = b; slope=0) or VERTICAL line (x = a; slope = "undefined")
* explain why the slope of a line can be determined by using any two points [ (x1, y1) ; (x2, y2) ] on that line (rise / run OR y2 ­ y1 / x2 ­ x1 )
* draw a line given its slope, "m", and a point on the
line (x , y)
* determine another point on a line given the
slope, "m", and a point, (x , y), on the line
* generalize and apply a rule for determining
whether two lines are parallel (same slopes) or perpendicular (opposite and reciprocal
slopes)
* solve a contextual problem involving slope
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Last week, we determined that:
SLOPES of PARALLEL lines are EQUAL. SLOPES of PERPENDICULAR lines are OPPOSITES ( + / ­ ) and RECIPROCALS (upside down) of each other. 4
HOMEWORK QUESTIONS???
(Pages 349 / 350, #9 and #11 TO #13)
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HOMEWORK QUESTIONS???
(Pages 349 / 350, #9 and #11 TO #13)
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EXAMPLE:
ABCD is a parallelogram. Is it a rectangle? Justify your answer.
PARALLELOGRAM:
A quadrilateral with
opposite sides parallel
and opposite angles
equal.
RECTANGLE:
A quadrilateral that
has four right angles.
RECTANGLE JUSTIFICATION:
In order for ABCD to be
a rectangle, AB and BC
must be perpendicular
lines; in other words,
they must intersect at
a 90 degree angle. We can determine this
by finding the slopes of
these two lines. As long
as these two slopes are
opposites and reciprocals,
ABCD IS a rectangle.
CONCLUSION: ABCD IS a rectangle. The slopes of AB (­4) and BC (1) are opposites and reciprocals; therefore, 4
AB and BC are perpendicular lines making angle B a 90 degree angles. Since angle B = angle D because of the fact ABCD is a parallelogram, angle D is also a 90 degree angle. Since AB and CD are parallel lines given, again, that ABCD is a parallelogram, the slope of CD is also ­4 making CD perpendicular to BC with THEIR opposite and reciprocal slopes. This makes angle C a 90 degree angle and, therefore, angle A a 90 degree angle given, again, that opposite angles in a parallelogram are equal. With four 90 degree angles, ABCD is most certainly a rectangle.
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SUGGESTED PRACTICE QUESTIONS:
(quiz tomorrow on Sections 6.1 / 6.2)
FPCM 10:
Page 350:
Page 351:
Page 353:
#16 & #17
#19
#1, #2, #4, #5, #7 & #8
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