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Understanding Polygons: Interior and Exterior Angles, Coordinate Relations, and Transformation

Learn about the properties of polygons, angle relationships, and coordinate transformations in Chapter 6. Explore how interior and exterior angles are related, calculate the sum of interior angles in polygons, and understand coordinate transformations. Test your knowledge with rhombus and quadrilateral characteristics.

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Understanding Polygons: Interior and Exterior Angles, Coordinate Relations, and Transformation

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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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