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Review Sheet Chapter Six

Review Sheet Chapter Six. Angles in Polygons : Interior angle + Exterior angle = 180 degrees (they form a linear pair!) Sum of interior angles = ( n – 2) x 180 for an n -sided polygon Interior angle = 180 – (360 / number of sides) Number of sides in a polygon = 360 / Exterior angle

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Review Sheet Chapter Six

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  1. Review Sheet Chapter Six Angles in Polygons: Interior angle + Exterior angle = 180 degrees (they form a linear pair!) Sum of interior angles = (n – 2) x 180 for an n-sided polygon Interior angle = 180 – (360 / number of sides) Number of sides in a polygon = 360 / Exterior angle Exterior angle = 360 / number of sides Quadrilateral Characteristics: Test Taking Tips: Remember midpoint formula (from chapter 1) and slope formula (from chapter 3) Use triangles (change in x and change in y) to plot slopes for parallelogram

  2. Polygons and Circles • SSM: • not much help Interior angle + exterior angle = 180 156 + x = 180 x = 24 360 = n  exterior angle 360 = 24 n 15 = n

  3. Ch 6 Coordinate Relations and Transformations • SSM: • rhombus: sides equal 9 Rhombus: all sides equal  6x – 5 = 4x + 13 6x = 4x + 18 2x = 18 x = 9

  4. Ch 6 Coordinate Relations and Transformations • SSM: • large obtuse angle • no real help Once around a point is 360. Interior angle of equilateral triangle is 60 and the interior angle of a nonagon is 140 (180 – Ext angle: ext angle = 360/9). Angle JKL = 360 – (140 + 60) = 360 – 200 = 160

  5. Ch 6 Coordinate Relations and Transformations • SSM: • medium acute angle • Eliminate C and D Angle DAE is complementary with angle DBC. 90 – 36 = 54.

  6. Ch 6 Coordinate Relations and Transformations • SSM: • Angle U is medium obtuse • Eliminate A, B and D A hexagon has a sum of its interior angles = 720 (from (n-2)180) 720 = 90 + 150 + 150 + 90 + x + x 720 = 480 + 2x 240 = 2x 120 = x

  7. Ch 6 Coordinate Relations and Transformations • SSM: • plot points • plot answers Rectangle’s diagonals bisect each other and are at the midpoint. Only answer A corresponds to another vertex. Use same concept as in chapter 1 finding the other endpoint.

  8. Ch 6 Coordinate Relations and Transformations • SSM: • small obtuse angle • eliminate C and D Once around a point is 360. Interior angle of octagon is 135 and the interior angle of a trapezoid is 125 (180 – 55 = 125). Angle x = 360 – (135 + 125) = 360 – 260 = 100

  9. Ch 6 Coordinate Relations and Transformations • SSM: • triangle, 3 sides, angles = 180 • add 180 for each additional side Sum of interior angles = (n – 2)180. Five vertices and 5 sides, so n = 5. (5 – 2) 180 = 3 180 = 540

  10. Ch 6 Coordinate Relations and Transformations • SSM: • plug answers in and look for an acute angle less than 62 Rectangles corner angles are 90 degrees and all angles inside a triangle add to 180, We get the following equation: 62 + 90 + 2x + 4 = 180 2x + 156 = 180 2x = 24 x = 12

  11. Ch 6 Coordinate Relations and Transformations • SSM: • draw each figure • diagonals perpendicular Opposite sides parallel and congruent is related to parallelograms. But parallelograms and rectangles don’t have perpendicular diagonals; only rhombi and squares have diagonals that are perpendicular.

  12. Ch 6 Coordinate Relations and Transformations • SSM: • medium obtuse angle (eliminate D) Quadrilateral ABCD’s angles sum up to 360. 360 = 90 + 120 + (2x + 30) + x 360 = 240 + 3x 120 = 3x 40 = x So angle DCE is a linear pair = 180 – 40 = 140

  13. Ch 6 Coordinate Relations and Transformations • SSM: • draw figure • see which are true are perpendicular bisect each other are congruent A square’s diagonals are perpendicular (from rhombus), bisect each other (from parallelogram) and are congruent (from rectangle)

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