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Chapter 7 Review

Chapter 7 Review. By Sarah & Gabby. 7-1 Parallel Lines and related Angles. A transversal is a line that intersects two coplanar lines at two distinct points. The blue line is a transversal. 7-1 Parallel Lines and related Angles.

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Chapter 7 Review

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  1. Chapter 7 Review By Sarah & Gabby

  2. 7-1 Parallel Lines and related Angles • A transversal is a line that intersects two coplanar lines at two distinct points. • The blue line is a transversal.

  3. 7-1 Parallel Lines and related Angles • Corresponding angles are always congruent. Think of them as “sliders”. They slide down a transversal and land on its corresponding angle. • <A & <B are corresponding angles.

  4. 7-1 Parallel Lines and Related Angles • Alternate interior angles are also always congruent. They are found inside the parallel lines and on opposite sides of the transversal. • <A & <D are alternate interior angles.

  5. 7-1 Parallel Lines and Related Angles • Same side interior angles are supplementary. They are located on the interior and on the same side of the transversal. • <3 and <5 are same side interior angles. • <4 and <6 are also same side interior angles.

  6. 7-2 Proving Lines Parallel • If two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel. • If <Q=<R, then AB ll CD.

  7. 7-2 Proving Two Lines Parallel • If two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel. • If <3=<6, then p ll q.

  8. 7-2 Proving Two Lines Parallel • If two lines are cut by a transversal so that a pair of same side interior angles are supplementary, then the lines are parallel. • If <4 and <6 are supplementary, then p ll q.

  9. Graphing Lines • The standard equation of a line in y-intercept form is: y=mx+b • By using this equation, you can tell if two lines are parallel, perpendicular, or neither, without graphing them. • For example, parallel lines have the same slope: y=5x+3 and y=5x+7 are parallel lines since they both have a slope of 5.

  10. Graphing Lines • You can also determine perpendicular lines. For example: y=3x-4 and y=-1/3x-7 are perpendicular because their slopes are negative reciprocals of each other. • If the slopes are not equal or negative reciprocals of each other, you cannot determine them to be parallel or perpendicular. Example: y=4x+7 and y=-6x-9 are neither parallel nor perpendicular.

  11. Graphing Lines • In order to graph the equation y=-2x+4, first you must graph the y intercept, which is 4. • Once you mark your point on the y-axis, you determine the slope. In this equation, the slope is -2 or -2/1. • When you graph a line, the slope is rise over run. Therefore, you would go 2 down since the slope is negative, followed by 1 to the right. After you’ve placed your points on the graph, you end up with a line that looks like this:

  12. Graphing Lines

  13. Determining Slope • To find the slope of a line we use the formula: • m=y2-y1 x2-x1 • Example: A(1,3) B(2,5) • m=5-3 2-1 • The slope is 2/1 or 2.

  14. BINGO GAME

  15. BINGO • Find the value of x. • ANSWER: x=65

  16. BINGO • Are the lines parallel, perpendicular, or neither? y=3x-4 y=-1/2x+3. • ANSWER: neither

  17. BINGO • Find the value of x. • ANSWER: x=21

  18. BINGO • Are the lines parallel, perpendicular, or neither? X=4 Y=-2 • ANSWER: perpendicular

  19. BINGO • Find the measure of <1. • ANSWER: <1=40

  20. BINGO • Find the slope of: • A(2,0) B(2,4) • ANSWER: undefined

  21. BINGO • Find the measure of angles 2 & 3. • ANSWER: <2=40 <3=140

  22. BINGO • If <2=85, find the m<6. • ANSWER: m<6=85

  23. BINGO • Determine the slope and tell if the lines are parallel, perpendicular or neither. • A(0,3) B(-2,3) and C(5,-1) D(5,3) • ANSWER: 0/-2 ; 4/0 ; perpendicular

  24. BINGO • Determine the slope of points A & B . • A(-3,5) B(2,3) • ANSWER: 2/-5

  25. BINGO • Find the measure of <H. • ANSWER: <H= 110

  26. BINGO • What type of angles are <1 and <5? • ANSWER: corresponding angles

  27. BINGO • Find the slope of: • A(-4,1) B(1,3) • ANSWER: -2/-5 (2/5)

  28. BINGO • What type of angles are <3 and <6? • ANSWER: alternate interior angles

  29. BINGO • What type of angles are <3 and <5? • ANSWER: same side interior angles

  30. BINGO • Give the angle to make the following true, <7=_______. • ANSWER: < 3

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