Classifying Two-Dimensional Figures

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

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.

Here is a list of the most basic polygons: Classifying 2-Dimensional Figures Here is a list of the most basic polygons: 3-sided Triangle 7-sided Septagon Quadrilateral 4-sided 8-sided Octagon Pentagon 5-sided 9-sided Nonagon 6-sided Hexagon 10-sided Decagon

Classifying Quadrilaterals

A main group of polygons are Properties of Quadrilaterals A main group of polygons are the quadrilaterals. All quadrilaterals have: 4 sides 4 angles (that add up to 360°)

Classifying Quadrilaterals We classify quadrilaterals based on whether or not they have certain properties: How many sets of parallel sides it has Parallel Line -Two lines on the same plane that will never cross. They are always the same distance apart.

Classifying Quadrilaterals We classify quadrilaterals based on whether or not they have certain properties: The number of congruent sides it has Congruent – having the same measure, indicated by hash lines These sides are congruent These sides are congruent

Classifying Quadrilaterals We classify quadrilaterals based on whether or not they have certain properties: If it contain right angles Right angles = 90 degrees, indicated by a square in the corner

Classifying Quadrilaterals Let’s classify quadrilaterals from those with the fewest properties to those with the most properties. Quadrilateral with one pair of parallel sides Quadrilateral with no parallel or congruent sides Trapezoid Basic Quadrilateral

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

Classifying Quadrilaterals A parallelogram A rectangle A rhombus A parallelogram 4 congruent sides □ □ Rhombus □ □ Square 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 triangle pentagon rectangle parallelogram right triangle octagon trapezoid square rhombus Higher Grounds Coffee 1. trapezoid triangle parallelogram Work Zone 4. F FA Future Farmers of America 3. pentagon 5. ITALIA World Cup 2014 Trail 3 6. trapezoid 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?

Classifying 2D Figures Match each term with one of the figures. B G F 1. Triangle _____ 2. Rhombus _____ 3. Pentagon _____ 4. Trapezoid ________ E C D 5. Octagon _____ 6. Parallelogram _____ 7. Quadrilateral _____ E A F C D 120° G B

Classifying Triangles

There are just a few basic ways that we classify or name triangles! Properties of Triangles All triangles have: 3 sides 3 angles (that add up to 180°) There are just a few basic ways that we classify or name triangles!

We classify or name triangles by their angles. Classifying Triangles We classify or name triangles by their angles. < 90° All angles Acute Triangle □ One 90° angle Right Triangle One angle > 90° Obtuse Triangle

We also classify triangles by their side lengths and angle measures. Classifying Triangles We also classify triangles by their side lengths and angle measures. 3 congruent sides All angles congruent Equilateral Triangle 2 congruent sides 2 congruent angles Isosceles Triangle No congruent sides No congruent angles Scalene Triangle

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