Does anyone want to classify my figure? Mikes Math Mall Slide 2 In life, we like to group objects in categories based on their properties. Placing objects into categories makes it easier to compare them with other objects. I struggle with this junk all the time! Really? How so? Im always wonderingcan a soft taco be grouped with a burrito? Or is a quesadilla just a smashed burrito sandwich? I feel your pain? Slide 3 Lets look at some vocabulary terms before we start classifying figures. Two-dimensional having a width and a height but flat like a piece of paper. One-dimension Two-dimensions Three-dimensions Polygon a two-dimensional shape made up of straight lines that are closed. Polygon Slide 4 Here is a list of the most basic polygons: Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon 3-sided 4-sided 5-sided 6-sided 7-sided 8-sided Slide 5 Congruent having the same measure Hash marks indicate sides with the same length. Angle arcs indicate angles of the same measure. Slide 6 Yep! I got it on sale! Part I Slide 7 All triangles have: 3 sides 3 interior angles (that add up to 180) Yeah, but arent there like a bazillion different kinds of triangles? I wouldnt say a bazillion! There are just a few basic ways that we classify or name triangles! Just a few? Why, are we counting? One must know what one is getting into before one gets into it, Professor! Just check this out! Slide 8 We classify or name triangles by their angles. Acute Triangle All angles less than 90 Obtuse Triangle One angle greater than 90 < 90 All angles One 90 angle One angle > 90 Right Triangle One 90 angle means 90 Slide 9 We also classify triangles by their side lengths and angle measures. Equilateral Triangle 3 congruent sides All angles congruent Isosceles Triangle 2 congruent sides 2 congruent angles Scalene Triangle No congruent sides No congruent angles Slide 10 Classify each triangle by ALL names that apply. 1. ____________________ 3. 140 ____________________ Right Isosc eles Acute Isosc eles Obtus e Scale ne Slide 11 This doesnt seem too rough, but Ive never seen a cute triangle? Thats not what acute actually means! Maybe we should just go take a look at some quadrilaterals now! Its nothing personal. I simply find triangles fairly unattractive. Im not paid enough! Are they cute? So, what do think about classifying triangles, Mr. Sparkles? Slide 12 Part II I know what youre thinking sweet lid, right? Slide 13 Another main group of polygons are the quadrilaterals. All quadrilaterals have: 4 sides 4 interior angles (that add up to 360) How can I classify these things when I dont even know what a cordlaratamal is? Have you ever heard of a square? Yeah, duh! Well, squares are quad-ri-lat-er-als! Just checking to see if youre awake! Slide 14 Lets classify quadrilaterals from those with the fewest properties to those with the most properties. Parallel Lines Two lines on the same plane that will never cross. They are always the same distance apart. Slide 15 By definition, rectangles are considered parallelograms. Why cant parallelograms be classified as rectangles? Parallelograms do not have 4 congruent angles. Slide 16 Why can we classify a square as a rectangle and a rhombus? A square is a parallelogram with 4 right angles (rectangle) A square is a parallelogram with 4 congruent sides (rhombus) Slide 17 Name each of the following polygons. ITALIA World Cup 2014 2014 WORD BANK equilateral triangle pentagon rectangle parallelogram right triangle octagon trapezoid square rhombus Coffee 1. 2. Future Farmers of America of America 3. Work Zone 4. 5. 6. trapezoid equilateral triangle parallelogram pentagon right triangle trapezoid Slide 18 Answer the following questions. 1. What do the hash marks indicate on the sides of polygons? 2. Whats the difference between a regular and irregular polygon? 3. By definition, we can classify all rectangles as parallelograms, but why cant we classify parallelograms as rectangles? 4. Whats the difference between an obtuse angle and an acute angle? Hash marks indicate that those side lengths are congruent. A regular polygon has sides and angles that are all congruent. An irregular polygon does not. A rectangle has two pairs of parallel sides and two pairs of congruent sides as defined by a parallelogram. However, a rectangle has four 90 right angles which is not included in the definition of a parallelogram. An obtuse angle is greater than 90, and an acute angle is less than 90. Slide 19 Match each term with one of the figures. 1. Scalene Obtuse Triangle _____ 2. Rhombus _____ 3. Regular Pentagon _____ 4. Trapezoid _____ 5. Isosceles Triangle _____ 6. Equilateral Triangle_____ 7. Octagon _____ 8. Parallelogram _____ 9. Irregular Quadrilateral _____ 120 A B C D E F G H I H G F A B I E C D Slide 20 So how do you feel about classifying two-dimensional figures, Sparky? I am a classifying polygaterals and quadrigonials beast, sir! Im not sure you Ill prove it! Ask me a question! Ok! How many sides does a heptagon have? Thats easy! Extinct dinosaurs dont have any sides! Promise me youll look over the notes! Mikes Math Mall Its a promise, sir!