Chapter 3: Parallel and Perpendicular Lines Lesson 1: Parallel Lines and Transversals.
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Chapter 3: Parallel and Perpendicular LinesLesson 1: Parallel Lines and TransversalsDefinitionsParallel lines ( || )- coplanar lines that do not intersect (arrows on lines indicate which sets are parallel to each other)Parallel planes- two or more planes that do not intersectSkew lines- lines that do not intersect but are not parallel (are not coplanar)Transversal- a line that intersects two or more lines in a plane at different pointsFrayer ModelAlternate Exterior AnglesAlternate Interior AnglesCorresponding AnglesConsecutive Interior AnglesPairs of angles formed by parallel lines and a transversal (see graphic organizer for examples)Exterior angles: outside the two parallel linesInterior angles: between the two parallel linesConsecutive Interior angles: between the two parallel lines, on the same side of the transversalAlternate Exterior angles: outside the two parallel lines, on different sides of the transversalAlternate Interior angles: between the two parallel lines, on different sides of the transversalCorresponding angles: one outside the parallel lines, one inside the parallel lines and both on the same side of the transversalC. Name a plane parallel to plane ABG.Classify the relationship between each set of angles as alternate interior, alternate exterior, corresponding, or consecutive interior anglesA. 2 and 6 B. 1 and 7C. 3 and 8D. 3 and 5A. A group of nature trails is shown. Identify the sets of lines to which line a is a transversal.B. A group of nature trails is shown. Identify the sets of lines to which line b is a transversal.C. A group of nature trails is shown. Identify the sets of lines to which line c is a transversal.Chapter 3: Parallel and Perpendicular LinesLesson 2: Angles and Parallel LinesIf two parallel lines are cut by a transversal, then (see graphic organizer)the alternate interior angles are congruentthe consecutive interior angles are supplementarythe alternate exterior angles are congruentthe corresponding angles are congruentIn a plane, if a line is perpendicular to one of the two parallel lines, then it is also perpendicular to the other line.A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used.B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used.A. In the figure, a || b and m18 = 42. Find m22.B. In the figure, a || b and m18 = 42. Find m25.A. ALGEBRA If m5 = 2x 10, and m7 = x + 15, find x.B. ALGEBRA If m4 = 4(y 25), and m8 = 4y, find y.ALGEBRA If m1 = 9x + 6, m2 = 2(5x 3), and m3 = 5y + 14, find x. B. ALGEBRA If m1 = 9x + 6, m2 = 2(5x 3), and m3 = 5y + 14, find y. Chapter 3: Parallel and Perpendicular LinesLesson 3: Slopes of LinesSlopeThe ratio of the vertical rise over the horizontal run Can be used to describe a rate of changeTwo non-vertical lines have the same slope if and only if they are parallelTwo non-vertical lines are perpendicular if and only if the product of their slopes is -1Foldable Step 1: fold the paper into 3 columns/sectionsStep 2: fold the top edge down about inch to form a place for titles. Unfold the paper and turn it vertically.Step 3: title the top row Slope, the middle row Slope-intercept form and the bottom row Point-slope formSlopeRise = 0 zero slope (horizontal line)Run = 0 undefined (vertical line)Parallel = same slope Perpendicular = one slope is the reciprocal and opposite sign of the otherEx: find the slope of a line containing (4, 6) and (-2, 8)Find the slope of the line.Find the slope of the line.Find the slope of the line.Find the slope of the line.Determine whether FG and HJ are parallel, perpendicular, or neither for F(1, 3), G(2, 1), H(5, 0), and J(6, 3). (DO NOT GRAPH TO FIGURE THIS OUT!!)Determine whether AB and CD are parallel, perpendicular, or neither for A(2, 1), B(4, 5), C(6, 1), and D(9, 2) Chapter 3: Parallel and Perpendicular LinesLesson 4: Equations of LinesSlope-intercept form:y = mx + b* This should be your middle row on the foldablePoint-slope form:* This should be your bottom row on the foldableWrite an equation in slope-intercept form of the line with slope of 6 and y-intercept of 3. Write the equation in slope-intercept form and thenWrite an equation in slope-intercept form for a line containing (4, 9) and (2, 0).Write an equation in point-slope form for a line containing (3, 7) and (1, 3).Chapter 3: Parallel and Perpendicular LinesLesson 5: Proving Lines ParallelTwo lines are parallel if they are cut by a transversal so that (see graphic organizer)Corresponding angles are congruentAlternate exterior angles are congruentConsecutive interior angles are supplementaryAlternate interior angles are congruentThey are both perpendicular to the transversalIf given a line and a point not on the line, there is exactly one line through that point that is parallel to the given lineB. Given m1 = 103 and m4 = 100, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer.A. Given 1 3, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer.A. Given 9 13, which segments are parallel?B. Given 2 5, which segments are parallel?Perpendicular Lines and DistanceThe shortest distance between a line and a point not on the line is the length of the perpendicular line connecting themEquidistant: the same distance- parallel lines are equidistant because they never get any closer or farther apartThe distance between two parallel lines is the distance between one line and any point on the other lineIn a plane, if two lines are equidistant from a third line, then the two lines are parallel to each other
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