1. Math 1 March 15 th WARM-UP: QUIZ TODAY!! In a triangle… 1.The three altitudes intersect at the ____________. 2.The three angle bisectors intersect at the __________. 3.The three medians intersect at the ____________. 4.The three perpendicular bisectors intersect at the ____. 5.S is the centroid in the triangle below. SV = 4, UW = 5, and QW = 21 Find the measure of: a) ST b) TW c) QS

2. Announcement for Freshman: You must pass your MATH class and your ENGLISH class to be promoted to 10 th grade. So, if you fail MATH OR ENGLISH, you will stay in 9 th grade next year.

3. More Important Terms EQUILATERAL - All sides are congruent EQUIANGULAR - All angles are congruent REGULAR - All sides and angles are congruent

4. Polygons are named by listing its vertices consecutively. AB ED C F

5. Polygons can be CONCAVE or CONVEX CONVEX CONCAVE

6. Ex. 3 Classify each polygon as convex or concave.

8. What is the sum of the measures of the interior angles of a triangle? 180° What is the sum of the measures of the interior angles of any quadrilateral?REVIEW: 180° 360°

9. # of sides # of triangles Sum of measures of interior angles 31 1(180) = 180 42 2(180) = 360 5 33(180) = 540 644(180) = 720 n n-2 (n-2)  180

10. If a convex polygon has n sides, then the sum of the measure of the interior angles is (n – 2)(180°)

11. Ex. 1 Use the regular pentagon to answer the questions. A)Find the sum of the measures of the interior angles. B)Find the measure of ONE interior angle 540° 108°

12. Two more important terms Exterior Angles Interior Angles

13. If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°. 1 2 3 4 5

14. 1 3 2

15. 1 3 2 4

16. Ex. 2 Find the measure of ONE exterior angle of a regular hexagon. 60°

17. Ex. 3 Find the measure of ONE exterior angle of a regular heptagon. 51.4°

18. Ex. 4 Each exterior angle of a polygon is 18 . How many sides does it have? n = 20

19. Ex. 5 The sum of the measures of five interior angles of a hexagon is 535. What is the measure of the sixth angle? 185°

20. Ex. 6 The measure of the exterior angle of a quadrilateral are x, 3x, 5x, and 3x. Find the measure of each angle. 30°, 90°, 150°, and 90°

21. Ex. 7 If each interior angle of a regular polygon is 150 , then how many sides does the polygon have? n = 12

22. Foldable for Formulas