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Transcript
Polygons, Triangles and Quadrilaterals Objective: Students will be able to define and identify types of polygons, triangles and quadrilaterals. What is a polygon? Closed 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 Triangles Triangles Quadrilater Quadrilateral al Pentagon Pentagon Hexagon Hexagon Heptagon Heptagon Octagon Octagon Nonagon Nonagon Decagon Decagon Undecagon Undecagon Dodecagon Dodecagon N-agon N-agon name sum of measure of each sum of measure of each interior interior angle if exterior exterior angle if a number of sum of measure of each interior sum of measure of each exterior number of angles regular polygon anglesangles angle regular poygon diagonals interior angles angle if regular polygon exterior if a regular poygon diagonals sides sides N 3 180 60 360 120 0 4 360 90 360 90 2 5 540 108 360 72 5 6 720 120 360 60 9 7 900 128.5714286 360 51.42857143 14 8 1080 135 360 45 20 9 1260 140 360 40 27 10 1440 144 360 36 35 11 1620 147.2727273 360 32.72727273 44 12 1800 150 360 30 54 180(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 Classify vs Naming Classify is when we use the type of angles and number of congruent sides Naming we use the vertices of the triangle Naming Polygons you need to go in order of vertices – either clockwise or counter clockwise, you can not skip over a vertex Consecutive vertices means one right after the other Congruent Polygons Polygons can be congruent but corresponding parts need to be congruent Corresponding – same location in the two polygons Congruent angles and sides Congruency Statement – name the polygons congruent in the correct order of congruent vertices Examples Naming and Congruency Statements 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 Objective: Students will be able to define and identify types of polygons, triangles and quadrilaterals. On a scale of 1 to 4 Do you feel we meet the objective for the day. If we did not meet the objective, what did we miss and how could I improve. Homework Due by end of class Wkst Aliens Wkst Airlines In your notes Pg 57 15,16,17 Pg 63 15 and 16 Pg 66 9 and 10