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Math 1 March 15 th

Math 1 March 15 th. WARM-UP: QUIZ TODAY!! In a triangle… The three altitudes intersect at the ____________. The three angle bisectors intersect at the __________. The three medians intersect at the ____________. The three perpendicular bisectors intersect at the ____.

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Math 1 March 15 th

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  1. Math 1 March 15th WARM-UP: QUIZ TODAY!! In a triangle… The three altitudes intersect at the ____________. The three angle bisectors intersect at the __________. The three medians intersect at the ____________. The three perpendicular bisectors intersect at the ____. 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 10th grade. • So, if you fail MATH OR ENGLISH, you will stay in 9th 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. A B C F E D

  5. Polygons can be CONCAVE or CONVEX CONCAVE CONVEX

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

  7. Diagonals & Angle Measures

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

  9. Sum of measures of interior angles # of triangles # of sides 1(180) = 180 3 1 2(180) = 360 4 2 3 3(180) = 540 5 6 4 4(180) = 720 n-2 (n-2) 180 n

  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. • Find the sum of the measures of the interior angles. • Find the measure of ONE interior angle 540° 108°

  12. Interior Angles Exterior Angles Two more important terms

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

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

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

  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

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