1. Classifying Quadrilaterals Quadrilateral -Four sided figure. Trapezoid -A quadrilateral with only one set of parallel sides. Parallelogram -A quadrilateral with two sets of parallel sides. Rectangle -A parallelogram with right angles. Rhombus -A parallelogram with equal sides. Square -A rectangle with equal sides or a rhombus with right angles. Objective - To name different types of Polygons.

2. Quadrilateral 4 sided figure Trapezoid Only 1 set of parallel sides Isosceles Trapezoid Parallelogram Two sets of parallel sides Rectangle Parallel- ogram with right angles Rhombus Parallel- ogram with equal sides Square Rhombus with right angles Rectangle with equal sides

3. State whether each statement is always true, sometimes true, or false. 1) A square is a rectangle. 2) A rectangle is a square. 3) All rectangles are squares. 4) All squares are parallelograms. 5) All quadrilaterals are rectangles. 6) A square is a trapezoid. 7) A parallelogram is a rectangle. Always True Sometimes True False Always True False Sometimes True

4. Make a Venn Diagram that accurately depicts the relationships between quadrilaterals, trapezoids, parallelograms, rhombuses, rectangles, and squares. Square Rectangle Rhombus Parallelogram Trapezoid Quadrilaterals

5. Give all the names that apply to the figure below. Circle the most specific name. 1) 2) 3) 4) Parallelogram, Quadrilateral Trapezoid, Quadrilateral 6 10 66 8 14 7 7 Quadrilateral, Parallelogram, Rhombus 33 33 Quadrilateral, Parallelogram Rectangle, Rhombus,, Square

6. What is a polygon? Polygon -A closed figure made up of line segments. Circle the polygons below. Regular Polygon - Polygon with all sides congruent and all angles congruent. Polygons

7. Regular Polygons Name # of sides Drawing Name Drawing 3Triangle Acute Equilateral 4Quadrilateral Square 5Pentagon Regular Pentagon 6Hexagon Regular Hexagon 8Octagon Regular Octagon 10Decagon Regular Decagon

8. Convex vs. Concave (non-convex) Convex - A polygon is convex if a segment connecting any two points within the figure is also fully contained within the figure. cave Convex Non-convex

11. Find the measure of each interior angle of a regular decagon. Step 1 Find the sum of the interior angle measures. Step 2 Find the measure of one interior angle. (n – 2)180° (10 – 2)180° = 1440° Polygon  Sum Thm. Substitute 10 for n and simplify. The int. s are , so divide by 10.

13. Example 4B: Finding Interior Angle Measures and Sums in Polygons Find the value of b in polygon FGHJKL. 15b° + 18b° + 33b° + 16b° + 10b° + 28b° = 360° Polygon Ext.  Sum Thm. 120b = 360Combine like terms. b = 3Divide both sides by 120.

14. Ann is making paper stars for party decorations. What is the measure of 1? 1 is an exterior angle of a regular pentagon. By the Polygon Exterior Angle Sum Theorem, the sum of the exterior angles measures is 360°. A regular pentagon has 5  ext. , so divide the sum by 5.

15. 1. Name the polygon by the number of its sides. Then tell whether the polygon is regular or irregular, concave or convex. 2. Find the sum of the interior angle measures of a convex 11-gon. nonagon; irregular; concave 1620° 3. Find the measure of each interior angle of a regular 18-gon. 4. Find the measure of each exterior angle of a regular 15-gon. 160° 24°