want to classify my figure? Does anyone want to classify my figure? Classifying Two-Dimensional Figures Made Easy ©Mike’s Math Mall

Classifying 2-Dimensional Figures 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’m always wondering…can a soft taco be grouped with a burrito? I feel your pain? I struggle with this junk all the time! Or is a quesadilla just a smashed burrito sandwich? Really? How so?

Classifying 2-Dimensional Figures Let’s 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. Polygon Two-dimensions Polygon – a two-dimensional shape made up of straight lines that are closed. One-dimension Three-dimensions

Here is a list of the most basic polygons: Classifying 2-Dimensional Figures Here is a list of the most basic polygons: Triangle 3-sided Hexagon 6-sided Quadrilateral 4-sided Heptagon 7-sided Pentagon 5-sided Octagon 8-sided

Polygons are either regular or irregular. Classifying 2-Dimensional Figures Polygons are either regular or irregular. This is a regular pentagon because ALL of its sides and angles are congruent. Congruent – having the same measure Hash marks indicate sides with the same length. Angle arcs indicate angles of the same measure. This is an irregular pentagon because some of its sides and angles are not congruent.

Part I Classifying Triangles Yep! I got it on sale!

Properties of Triangles All triangles have: 3 sides 3 interior angles (that add up to 180°) Yeah, but aren’t there like a bazillion different kinds of triangles? Just a few? One must know what one is getting into before one gets into it, Professor! I wouldn’t say a bazillion! Why, are we counting? There are just a few basic ways that we classify or name triangles! Just check this out!

We classify or name triangles by their angles. Classifying Triangles We classify or name triangles by their angles. < 90° All angles Acute Triangle All angles less than 90° Right Triangle One 90° angle “□” means 90° □ One 90° angle Obtuse Triangle One angle greater than 90° One angle > 90°

We also classify triangles by their side lengths and angle measures. Classifying Triangles 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

Classify each triangle by ALL names that apply. Name that Triangle! Classify each triangle by ALL names that apply. 2. ____________________ Acute Isosceles □ 1. ____________________ 3. 140° ____________________ Right Isosceles Obtuse Scalene

So, what do think about classifying triangles, Mr. Sparkles? It’s nothing personal. I simply find triangles fairly unattractive. This doesn’t seem too rough, but I’ve never seen a cute triangle? Are they cute? That’s not what “acute” actually means! I’m not paid enough! Maybe we should just go take a look at some quadrilaterals now!

Quadrilaterals Classifying Part II I know what you’re thinking… sweet lid, right?

Another main group of polygons are Properties of Quadrilaterals 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 don’t even know what a cordlaratamal is? Yeah, duh! Just checking to see if you’re awake! Have you ever heard of a square? Well, squares are quad-ri-lat-er-als!

Classifying Quadrilaterals Let’s classify quadrilaterals from those with the fewest properties to those with the most properties. Basic Quadrilateral 4-sided polygon Trapezoid Quadrilateral with one pair of parallel sides Parallel Lines – Two lines on the same plane that will never cross. They are always the same distance apart.

Classifying Quadrilaterals Parallelogram Two pairs of parallel sides Opposite sides congruent Rectangle A parallelogram Four 90° angles □ □ □ □ By definition, rectangles are considered parallelograms. Why can’t parallelograms be classified as rectangles? Parallelograms do not have 4 congruent angles.

Classifying Quadrilaterals Square A parallelogram A rectangle A rhombus Rhombus A parallelogram 4 congruent sides □ □ □ □ 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)

Trail 3 Classifying 2-Dimensional Figures Higher Grounds ITALIA Work F Name each of the following polygons. 2. YIELD WORD BANK equilateral triangle pentagon rectangle parallelogram right triangle octagon trapezoid square rhombus Higher Grounds Coffee 1. trapezoid equilateral triangle parallelogram Work Zone 4. F FA Future Farmers of America 3. pentagon 5. ITALIA World Cup 2014 Trail 3 6. trapezoid right triangle

Classifying 2-Dimensional Figures Answer the following questions. 1. What do the “hash marks” indicate on the sides of polygons? Hash marks indicate that those side lengths are congruent. 2. What’s the difference between a regular and irregular polygon? A regular polygon has sides and angles that are all congruent. An irregular polygon does not. 3. By definition, we can classify all rectangles as parallelograms, but why can’t we classify parallelograms as rectangles? 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. 4. What’s the difference between an obtuse angle and an acute angle? An obtuse angle is greater than 90°, and an acute angle is less than 90°.

Classifying 2-Dimensional Figures Match each term with one of the figures. 1. Scalene Obtuse Triangle _____ 2. Rhombus _____ 3. Regular Pentagon _____ H G F 4. Trapezoid _____ 5. Isosceles Triangle _____ 6. Equilateral Triangle_____ A B I 7. Octagon _____ 8. Parallelogram _____ 9. Irregular Quadrilateral _____ E C D I A E F C D B 120° G H

So how do you feel about classifying two-dimensional figures, Sparky? Classifying Quadrilaterals So how do you feel about classifying two-dimensional figures, Sparky? I’ll prove it! Ask me a question! I am a classifying polygaterals and quadrigonials beast, sir! It’s a promise, sir! That’s easy! Extinct dinosaurs don’t have any sides! I’m not sure you… Promise me you’ll look over the notes! Ok! How many sides does a heptagon have? ©Mike’s Math Mall