Transcript Polygons
Polygons Triangles and Quadrilaterals What is a polygon? Close figure At least 3 sides Line segments are sides Sides meet is call a vertex More Polygon Terms Diagonal – connects two non consecutive vertices Concave – at least one diagonal outside polygon, dented in Convex – no diagonals outside polygon Perimeter – distance around polygon Area – space polygon covers up Define these types of Polygons pg 56 Equilateral All the sides of the polygon are congruent Equiangular All the interior angles of the polygon are congruent Regular All sides are congruent and all angles are congruent Types and prop of polygons name sum of interior angles sides measure of each interior angle if regular polygon sum of exterior angles measure of each exterior angle if a regular poygon number of diagonals Triangles 3 180 60 360 120 0 Quadrilateral 4 360 90 360 90 2 Pentagon 5 540 108 360 72 5 Hexagon 6 720 120 360 60 9 Heptagon 7 900 128.5714286 360 51.42857143 14 Octagon 8 1080 135 360 45 20 Nonagon 9 1260 140 360 40 27 Decagon 10 1440 144 360 36 35 Undecagon 11 1620 147.2727273 360 32.72727273 44 Dodecagon 12 1800 150 360 30 54 N-agon N 180(n-3) sum/n 360 360/n n(n-3)/2 Triangles – define the following pg 60 Right Has only one right angle In some case why can it have only one of that type of angle? Acute All 3 angles are acute angles Triangles interior angles add up to 180 and has 3 angles, if it had 2 right angles it is already at 180 and if it had 2 obtuse angles it would be over 180 Obtuse Has only one obtuse angle Notice the names of all these triangles deal with the type(s) of angle the triangle has More triangles pg 61 Scalene No sides congruent Isosceles 2 congruent sides, also has two congruent base angles Equilateral All sides are congruent Notice all these triangles are named based on sides congruent When naming a triangle you need to use both the name for type of angle and number of congruent sides Quadrilaterals define and list properties pg 64 Parallelogram Rectangle 2 pairs of parallel sides Opposite sides congruent Opposite angles congruent Consecutive angles supplementary Diagonals All properties of a parallelogram and All angles 90 degrees Rhombus All properties of a parallelogram and all sides congruent Square All properties of a parallelogram and all sides congruent and all angles 90 degrees Trapezoid 1 pair of parallel sides, there are 3 types we will discuss later Kite 2 pairs of congruent consecutive sides, 1 pair of congruent angles Quadrilaterals We will go into more depth with these shapes and come up with some additional properties as well Homework Pg 57 11,15,17 Pg 62 1-4 and 17-21 Pg 66 1-6