Review Sheet Chapter Three k l 1 2 3 4 5 6 7 8 Special Angle Pairs: Alternate Interior: (if //, then angles equal) 3 and 6 or 4 and 5 Alternate Exterior: (if //, then angles equal) 1 and 8 or 2 and 7 Corresponding: (if //, then angles equal) 1 and 5 or 3 and 7 or 2 and 6 or 4 and 8 Consecutive Interior: (if //, then angles add to 180) 3 and 5 or 4 and 6 Slopes Slope is change in y / change in x Parallel lines have the same slope slope = 3  parallel slope = 3 Perpendicular lines have negative inverse (reciprocal) slopes slope = 3  perpendicular slope = -1/3 Slope – Intercept Form: y = mx + b Point Slope Form: y – y1 = m(x – x1) Use Pythagorean triangles to work with slope m = y / x = 3/7 Test Taking Tips: Stop and think – don’t hurry through; Use graph paper to draw things Angle = Angle or Angle + Angle = 180 solves 90% of angle problems Acute = Acute or Obtuse = Obtuse or Acute + Obtuse = 180 Alternate – opposites sides of transversal t C’s – same side of transversal t y x 3 7 slope of solid line: 3/7 slope of  line: -7/3

Must use a and b and only one transversal Ch 3 Coordinate Relations and Transformations SSM: Must use a and b and only one transversal Option B shows consecutive “exterior” angles which are supplementary Option D shows corresponding angles between c and d.

x is a medium to large acute angle Ch 3 Coordinate Relations and Transformations SSM: x is a medium to large acute angle Corresponding angles of parallel lines are congruent

SSM: plot points use slope definition Ch 3 Coordinate Relations and Transformations SSM: plot points use slope definition Parallel lines have the same slope. Use points given to figure out the slope of line t (rise = -8 and run = 16), which is -1/2. Use that slope and rise/run to draw a line through point P and plot a point along that line.

3x + 14 = 143 (alternate exterior angles) 3x = 129 x = 43 Ch 3 Coordinate Relations and Transformations SSM: by eyes: angles equal 43 3x + 14 = 143 (alternate exterior angles) 3x = 129 x = 43

slope = m = ------------- = ------------- = 1/2 5 – (-3) 8 Ch 3 Coordinate Relations and Transformations SSM: draw points on graph find slope 7 – 3 4 slope = m = ------------- = ------------- = 1/2 5 – (-3) 8

Angle CBA is a large obtuse angle Ch 3 Coordinate Relations and Transformations SSM: Angle CBA is a large obtuse angle Angle CBA = angle ABH + angle HBC = 90 + supplementary with 115 (consecutive interior) = 90 + 65 = 155

parallel lines have same slope rise 3 Ch 3 Reasoning, Lines, and Transformations SSM: parallel lines have same slope rise 3 slope = m = ----------- = --------- run 7

two pairs of segments parallel Ch 3 Reasoning, Lines, and Transformations SSM: two pairs of segments parallel Regular quadrilateral is a square and has four lines of symmetry Even numbered regular polygons have a point of symmetry

draw line on graph paper Ch 3 Reasoning, Lines, and Transformations SSM: draw line on graph paper draw answers and check with scrap paper corner Find slope of line k (rise/run = 6/4), then flip and negate it (-run/rise = -4/6). Compare with slopes of the answers.

find equal special angle pairs Ch 3 Reasoning, Lines, and Transformations SSM: all acute measures find equal special angle pairs Angles between m and n are alternate interior angles for both transversal p and q. Angles between p and q would be supplementary angle pairs if parallel

25 SSM: no help 3x + 5 = 180 – (61 + 39) 3x + 5 = 80 3x = 75 x = 25 Ch 3 Reasoning, Lines, and Transformations SSM: no help 25 3x + 5 = 180 – (61 + 39) 3x + 5 = 80 3x = 75 x = 25

eyes tell us that x is a medium acute angle measure opposite sides Ch 3 Triangles SSM: eyes tell us that x is a medium acute angle measure opposite sides Other acute angle in triangle containing x is supplementary with 132 (=48) . Angle x and that angle are complementary (x + 48 = 90; so x = 42)