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Problem of the Day (Monday)

Problem of the Day (Monday). Alternate Interior Angles? 3 & 6, 4 & 5 1 & 4, 2 & 3, 5 & 8, 7 & 6 1 & 5, 2 & 6, 3 & 7, 4 & 8 1 & 8, 2 & 7. Angles Review. Corresponding Angles? 1 & 2, 2 & 4, 3 & 4, 1 & 3 6 & 5, 6 & 8, 7 & 8, 5 & 7 1 & 4, 2 & 3, 5 & 8, 7 & 6 1 & 5, 2 & 6, 3 & 7, 4 & 8

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Problem of the Day (Monday)

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  1. Problem of the Day (Monday) • Alternate Interior Angles? • 3 & 6, 4 & 5 • 1 & 4, 2 & 3, 5 & 8, 7 & 6 • 1 & 5, 2 & 6, 3 & 7, 4 & 8 • 1 & 8, 2 & 7

  2. Angles Review Corresponding Angles? • 1 & 2, 2 & 4, 3 & 4, 1 & 3 6 & 5, 6 & 8, 7 & 8, 5 & 7 • 1 & 4, 2 & 3, 5 & 8, 7 & 6 • 1 & 5, 2 & 6, 3 & 7, 4 & 8 • 1 & 8, 2 & 7 1 2 3 4 5 6 7 8

  3. Supplementary Angles? • 1 & 2, 2 & 4, 3 & 4, 1 & 3 • 6 & 5, 6 & 8, 7 & 8, 5 & 7 • 1 & 4, 2 & 3, 5 & 8, 7 & 6 • 1 & 5, 2 & 6, 3 & 7, 4 & 8 • 1 & 8, 2 & 7

  4. Alternate Exterior Angles? • 1 & 2, 2 & 4, 3 & 4, 1 & 3 • 6 & 5, 6 & 8, 7 & 8, 5 & 7 • 1 & 4, 2 & 3, 5 & 8, 7 & 6 • 1 & 5, 2 & 6, 3 & 7, 4 & 8 • 1 & 8, 2 & 7

  5. Vertical Angles? • 1 & 2, 2 & 4, 3 & 4, 1 & 3 • 6 & 5, 6 & 8, 7 & 8, 5 & 7 • 1 & 4, 2 & 3, 5 & 8, 7 & 6 • 1 & 5, 2 & 6, 3 & 7, 4 & 8 • 1 & 8, 2 & 7

  6. Polygon: Closed figure Regular Polygon: All sides are equal

  7. Triangles Everywhere

  8. Problem of the Day (Tuesday) What is the measure of angle x? • 720° • 120° • 360° • 60° x

  9. A regular pentagon: • What is the sum of the interior angles? • What is the measure of each interior angle? • What is the sum of the exterior angles? • What is the measure of each exterior angle?

  10. An irregular pentagon What is the measure of the missing angle? 90˚ 130˚ ? 90˚ 130˚

  11. A regular hexagon: • What is the sum of the interior angles?

  12. What is the measure of the missing angle? 90˚ 120˚ 170˚ 100˚ 130˚ ?

  13. A regular octagon: • What is the sum of the interior angles? • What is the measure of each interior angle? • What is the sum of the exterior angles? • What is the measure of each exterior angle?

  14. A regular decagon: • What is the sum of the interior angles? • What is the measure of each interior angle? • What is the sum of the exterior angles? • What is the measure of each exterior angle?

  15. Name__________________ *You may only assume that the pentagon and hexagon are regular. a = _____ b = _____ c = _____ d = _____ e = _____ f = _____ g = _____ h = _____ i = _____ j = _____ k = _____ l = _____ m = _____ n = _____ o = _____ p = _____ q = _____ r = _____ s = _____ t = _____ u = _____ v = _____ w = _____ x = _____ Missing Angles Challenge l m h j g b k c n q t s i a o p r u v d x 110° e 45° f

  16. Learning Target I can… Find the exterior angles of any polygon

  17. Exterior Angles of a Polygon

  18. Level Five – Find the missing angles 1. 3. b a 2. 4. 34˚ a b

  19. Missing Angles m n The lines m and n are parallel What is the measure angle b? What is the measure of angle a? What is the measure of angle g? What is the measure of angle f? a 98° d f b c e g

  20. Create your own puzzle Rules: • You must use at least 2 regular polygons • Angle measures must be close (they do not have to be perfectly drawn to scale) • You must use a ruler • You must include 3 of the following: complementary angles, supplementary angles, interior angles, exterior angles, corresponding angles, vertical angles

  21. Problem of the Day (Tuesday) What is the measure of angle x? • 720° • 120° • 360° • 60° x

  22. A regular pentagon: • What is the sum of the interior angles? • What is the measure of each interior angle? • What is the sum of the exterior angles? • What is the measure of each exterior angle?

  23. Congruent Triangles • All sides are congruent and all angles are congruent H L K J I G

  24. Congruent Triangles

  25. SSS B E A C F D

  26. SAS H L K J I G

  27. ASA

  28. AAS

  29. Q EAngle SQVTSide Q TAngle QPEYSide QRTUSide Q YAngle QPR EYT by ASA. SQR VTU by SAS. Congruent Polygons Show that each pair of triangles is congruent. a. b.

  30. Does AAA guarantee that two triangles are congruent? Why or why not? No Same angles, different sizes Example: 80° 80° 50° 50° 50° 50°

  31. J H Both are right angles. JI HI Both measure 48 ft. KIJ GIH They are vertical angles. So ∆GHI ∆ JI by ASA Corresponding parts of congruent triangles are congruent. JK corresponds to HG, so JK is 36 ft. Congruent Polygons A surveyor drew the diagram below to find the distance from J to I across the canyon. Show that GHIKJI. Then find JK.

  32. Congruent Polygons Use ABC and XYZ to answer the questions. 1.Suppose AC=XZ, AB = XY, and BC = YZ. Write a congruence statement for the figures. 2.Suppose ABC and XYZ are congruent. If AB = 5 cm, BC = 8 cm, and AC = 10 cm, find XZ. 3. Suppose BY, AX, and ABXY. Why is ABCXYZ? ∆ABC∆XYZ 10 cm ASA

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