1. 1.5: Describe Angle Pair Relationships 1.6: Classify Polygons Objectives: 1.To use special angle relationships to find angle measures 2.To define, name, and classify polygons

2. Vocabulary (make sure you know these) ComplementarySupplementaryLinear Pair Vertical AnglesPolygonDiagonal (n.) ConvexConcaveEquilateral EquiangularRegular Define these in your notebook

3. C Comes Before S…

4. Example 1a 1.Given that <1 is a complement of <2 and m<1 = 68°, find m<2. 2.Given that <3 is a supplement of <4 and m<3 = 56°, find m<4. 22 0 124 0

5. Example 1b 1.What is the sum of complementary angles in radians? 2.What is the sum of supplementary angles in radians? 3.What is complement for the angle that measures π /3? 4.What is the supplement for the angle that measures 3 π /4? Π 2 Π Π6Π6 Π 4

6. Example 2 Let <A and <B be complementary angles and let m<A = (2x 2 + 35)° and m<B = (x + 10)°. What is (are) the value(s) of x? What are the measures of the angles? Set up the equation and solve X = 4.5 or -5 m<A = 14.5 or 85 m<B = 75.5 or 5 Check to make sure the sum is 90

7. Linear Pairs of Angles

8. linear pairTwo adjacent angles form a linear pair if their noncommon sides are opposite rays. supplementaryThe angles in a linear pair are supplementary.

9. Vertical Angles

10. vertical anglesTwo nonadjacent angles are vertical angles if their sides form two pairs of opposite rays. Vertical angles are formed by two intersecting lines. Check them out HEREHERE

11. Example 3 Identify all of the linear pairs of angles and all of the vertical angles in the figure.

12. Example 4: SAT In the figure and, what is the value of x ? x=18, y=90 and z=72 HOW HOW did I do that?

13. 3-D Rendering 3-D rendering in digital graphics is based upon polygons.

14. 3-D Rendering The higher the polygon count, the smoother the surface. –Tomb Raider (1996)

15. 3-D Rendering The higher the polygon count, the smoother the surface. –Tomb Raider Underworld (2008)

16. What Makes a Polygon? So, what makes a polygon a polygon?

17. Polygons polygon sides vertices A closed plane figure is a polygon if it is formed by 3 or more line segments (sides), joined endpoint to endpoint (vertices) with each side intersecting exactly two others.

18. Parts of a Polygon What’s the name of this polygon? Consecutive Angles Consecutive Vertices Consecutive Sides

19. Example 5 Why are the following not polygons?

20. Names of Polygons (memorize these) Polygons come in many flavors. They are classified by the number of sides they have. A polygon with more than 12 sides is commonly called an n -gon, where n is the number of sides. SidesName 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 7Heptagon 8Octagon 9Nonagon 10Decagon 11Undecagon 12Dodecagon

21. Names of Polygons SidesName 3Triangle 4Quadrilateral* 5Pentagon 6Hexagon 7Heptagon 8Octagon 9Nonagon 10Decagon 11Undecagon 12Dodecagon SidesName 13Tridecagon 14Tetradecagon 15Pentadecagon 16Hexadecagon 17Heptadecaton 18Octadecagon 19Nonadecagon 20Icosagon 100Hectagon 1,000,000Hecatommyriagon *Also called a Tetragon

22. Example 6 Name each polygon. quadrilateral hexagon

23. Example 7 When you buy a 42” television, how or where is that 42 inches measured? 42”

24. Diagonal

25. Diagonal diagonal A diagonal is a line segment that joins two nonconsecutive vertices of a polygon.

26. Example 8 How many diagonals are there in an octagon? (Do you really want to draw that? Heck no! In your notebook make a table and find a pattern!)

27. Convex & Concave Polygons

28. Convex polygons Convex polygons have all their diagonals in the interior of the polygon. Concave polygons Concave polygons have at least one diagonal on the exterior of the polygon.

29. Example 9 Tell whether the figure is a polygon and whether it is convex or concave.

30. Equilateral Polygon equilateral polygon An equilateral polygon is a polygon in which all of its sides are congruent.

31. Equiangular Polygon equiangular polygon An equiangular polygon is a polygon in which all its interior angles are congruent.

32. Regular Polygon regular polygon A regular polygon is a polygon that is equilateral and equiangular.

33. Example 10 Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning.

34. Example 11: SAT In the figure, RS = ST and the coordinates of S are ( k, 3). What is the value of k ? -3

35. Example 12 Given that the figure is regular, find the values of x and y. x=12, y=8