1. Bell Work 3/4/13 Find the measure of x in each triangle 1) Use Special Right Triangles to solve a)b) 2)Use Trig Ratios to solve for the missing side a)b)

2. Outcomes I will be able to: 1) Use properties of special right triangles 2) Define and name a polygon 3) Determine if a polygon is convex or concave 4) Determine the measure of all the angles inside a quadrilateral

3. 6.1 Polygons sides vertexvertices ABCDEor DCBAE

4. Example 1 State whether the figure is a polygon

5. Names of Polygons Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon N-gon

6. Types of Polygons Convex: A polygon in which no line that contains a side includes a point inside the polygon. (In other words, extend the sides of the polygon. If it crosses inside the polygon, it is not convex!) Example: Concave: A polygon that is not convex. (Notice it caves in!) Example:

7. On Your OWN-Try Examples 1-3 1) Draw a convex polygon 2) Draw a concave polygon Convex Quadrilateral Concave Pentagon

8. Types of Polygons Equilateral Polygon: A polygon with all sides congruent. Equiangular Polygon: A polygon with all angles congruent. Regular Polygon: A polygon with both equilateral and equiangular.

9. Examples No, equilateral only No, equiangular only

10. Diagonal Example: Draw all of the diagonals for this hexagon non-consecutive vertices

11. Quadrilateral Sum 360° Angle1 + Angle2 + Angle3 + Angle4 = 360 x + 55 + x + 55 = 360 2x + 110 = 360 -110 -110 2x = 250 x = 125

12. Quadrilateral Sum x + x – 20 + x + 80 = 360 x = 100 No, because not all the angles are the same Is it regular?

13. On Your OWN Try Example 3 3) Solve for x x = 20

14. Parallelograms Parallelogram: A quadrilateral with both pairs of opposite sides parallel ***Arrows must be present to indicate that the lines are parallel

15. Theorems about parallelograms If a quadrilateral is a parallelogram then it is: Congruent PS congruent to QR and PQ congruent to SR

16. Theorems about Parallelograms Congruent <P and <R are congruent <S and <Q are congruent

17. Theorems about Parallelograms supplementary P + S = 180 Q + R = 180 and P + Q = 180 S + R = 180

18. Theorems about Parallelograms bisect each other PM congruent to MR and SM congruent to MQ

19. Examples

20. ***Hint: It might help drawing a quadrilateral. Then look at the angles.

21. Examples

22. Exit Quiz 1) Using what we know about quadrilaterals find the value of x 2) Using what we know about parallelograms, find the value of x, y, and z