* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download All About Polygons and Quadrilaterals
Survey
Document related concepts
Rotation formalisms in three dimensions wikipedia , lookup
Duality (projective geometry) wikipedia , lookup
Plane of rotation wikipedia , lookup
Technical drawing wikipedia , lookup
Perceived visual angle wikipedia , lookup
Line (geometry) wikipedia , lookup
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
Multilateration wikipedia , lookup
Trigonometric functions wikipedia , lookup
Transcript
All About Polygons and Quadrilaterals Mackenzie Simonsen Polygons 1 • 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. Angles of Polygons Interior • 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 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 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 ngon are 2,340º, how many sides are in this polygon? • There are 15 sides in this polygon (n - 2)180 = 2340 180 n - 2 = 13 n = 15 Parallelograms Properties • 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 Picture Angles 3 Angles 3 Diagonals 3 Properties • 4 right angles • Opposite sides are congruent • Diagonals are congruent 4 Picture • Find the measure of the missing angle • m<1= 90º 4 • Find the value of x. • X= 30 • Find the length of side DB. 4 Rhombus Properties • Diagonals are perpendicular • All sides are congruent • Diagonals bisect angles making them congruent 5 • ANGLES • Find the measure of angle one • M<1= 90º Rhombus • ANGLES • Find the measure of angle 2 • m<2= 25º 5 • DIAGONALS • Find the length of LN • 4x-1=3x+2 • X=3 • LN= 22 1. 4 right angles 2. All sides are congruent 3. Is both a rhombus and a rectangle 6 Trapezoids Regular • One set of parallel lines • Midsegment is equal to 1/2(top base x bottom base) • Midsegment is parallel to the bases 7 Isosceles • One set of parallel lines • Legs are congruent • Base angles are congruent • Diagonals are congruent Trapezoid/ Isosceles Trapezoid x y z y= 1 7 x · z) ( 2 Trapezoids Angles • Find the measure of angle 1 and 2 • 180º - 56º= 124º • M<1= 124º • M<2=56º Angles • Find the measure of angles 1 and 2 • M<1= 23º • M<2= 157º • 180º - 157º = 23º 1 56º 7 2 2 1 157º • Find x and the measure of side EF 180 13 A 4x- 15 B 4x -15 + 5x -10 ) 2( 4x = 4x -15 + 5x -10 2x = 1 4x = 9x - 25 E 2x 25 = 5x F x=5 2·5 =10 5x-10 D 7 EF= 10 C Median