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All About Polygons and Quadrilaterals

All About Polygons and Quadrilaterals. Mackenzie Simonsen. Polygons. Triangle- A plane figure with three straight sides and three angles. A way to remember a triangle is that tri- means three and a tri angle has three sides.

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All About Polygons and Quadrilaterals

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  1. All About Polygons and Quadrilaterals Mackenzie Simonsen

  2. Polygons • Triangle- A plane figure with three straight sides and three angles. A way to remember a triangle is that tri- means three and a triangle has three sides. • Quadrilateral- A plane figure with 4 straight sides and 4 angles. A way to remember is that quad- means 4. • Pentagon- A plane figure with 5 straight side and 5 angles. A way to remember is the Pentagon in Washington D.C., it have five sides. • Hexagon- A plane figure with 6 straight sides and 6 angles. A way to remember is know that hex- means six. • Heptagon- A plane figure with 7 straight sides and 7 angles. To remember heptagon you only have to know all the others. Like process of elimination. • Octagon- A plane figure with 8 straight sides and 8 angles. To remember and octagon just think of a stop sign, they are all octagons. • Nonagon- A plane figure with 9 straight sides and 9 angles. Nonagon is the only –gon that starts with the letter n, nine is the only singe digit number that starts with the letter n. • Decagon- A plane figure with 10 straight sides and 10 angles. When counting to ten in Spanish, 10 starts with a d and so does decagon. 1

  3. Angles of Polygons Interior Exterior All exterior angles add up to 360º. The answer is always 360º. Find one angle by dividing 360º by the number of sides. Find the measure of one exterior angle of an octagon. 360º/ 8= 45º • To find the sum of the interior angle take the number of sides on the polygon the subtract two from that number and multiply by 180º. Find the sum of the interior angles of an octagon. Use the equation (n-2)180. (8-2)180= 6*180= 1080º in an octagon. • To find one interior angle take the final number from the first step and divide it by the number of sides Find the measure of one interior angle of an octagon. (8-2)180= 6*180= 1080º / 8= 135º in one interior angle of an octagon. 2

  4. How to Find the Number of Sides • When given the sum of the interior angle measure use the equation: (n-2)180 • EXAMPLE: The sum of the interior angles of an n-gon are 2,340º, how many sides are in this polygon? • There are 15 sides in this polygon

  5. Parallelograms Properties Picture • Both sets of opposites sides are congruent and parallel • Corresponding angles add up to 180º • Opposite angles are congruent • Diagonals bisect each other and the parallelogram • It is a quadrilateral. 3

  6. Angles 3

  7. Angles 3

  8. Diagonals 3

  9. Rectangles Properties Picture • 4 right angles • Opposite sides are congruent • Diagonals are congruent 4

  10. Angles of a Rectangle • Find the value of x. • X= 30 • Find the measure of the missing angle • m<1= 90º 4

  11. Diagonals of a Rectangle • Find the length of side DB. 4

  12. Rhombus Properties • Diagonals are perpendicular • All sides are congruent • Diagonals bisect angles making them congruent • ANGLES • Find the measure of angle one • M<1= 90º 5

  13. Rhombus • ANGLES • Find the measure of angle 2 • m<2= 25º • DIAGONALS • Find the length of LN • 4x-1=3x+2 • X=3 • LN= 22 5

  14. Squares 4 right angles All sides are congruent Is both a rhombus and a rectangle 6

  15. Trapezoids Regular Isosceles One set of parallel lines Legs are congruent Base angles are congruent Diagonals are congruent • One set of parallel lines • Midsegment is equal to 1/2(top base x bottom base) • Midsegment is parallel to the bases 7

  16. Trapezoid/ Isosceles Trapezoid x y z 7

  17. Trapezoids Angles Angles Find the measure of angles 1 and 2 M<1= 23º M<2= 157º 180º - 157º = 23º • Find the measure of angle 1 and 2 • 180º - 56º= 124º • M<1= 124º • M<2=56º 1 157º 2 56º 2 1 7

  18. Median B A 4x- 15 • Find x and the measure of side EF E 2x F EF= 10 5x-10 C D 7

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