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Exterior Angles of Polygons by Heather Pierce

Exterior Angles of Polygons by Heather Pierce
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2018-12-04 23:40
PolygonAngleGeometric Construction
This example demonstrates the properties and calculations of exterior angles in polygons. Key math concepts include the exterior angle sum theorem and the relationship between interior and exterior angles. Construction highlights involve GeoGebra commands such as Dilate, Ray, Segment, Min, Circle, Intersect, CircleSector, Vector, and Translate, with objects like TC, J, d, TC', TB, TB', TA, TA', tf, tg, th, ti, tj, tk, ta, tc, te, tp, TD, TE, TF, TG, TH, TI, tsec1, tsec2, tu, tsec3, tsec1', tv, tsec2', tw, tsec3', triangle, quadrilateral, pentagon, hexagon, button1, QA, QB. Suitable for middle school students and above learning polygon geometry or for classroom demonstrations.

GeoGebra Commands & Parameters

  1. Dilate(TC, If[0 < d ≤ 1, 1 - d, 0], J) → TC'
  2. Dilate(TB, If[0 < d ≤ 1, 1 - d, 0], J) → TB'
  3. Dilate(TA, If[0 < d ≤ 1, 1 - d, 0], J) → TA'
  4. Ray(TA, TB) → tf
  5. Ray(TB, TC) → tg
  6. Ray(TC, TA) → th
  7. Segment(TA, TB) → ti
  8. Segment(TB, TC) → tj
  9. Segment(TC, TA) → tk
  10. Min({ti, tj, tk}) → ta
  11. Circle(TA, (0.15 * ta)) → tc
  12. Circle(TB, (0.15 * ta)) → te
  13. Circle(TC, (0.15 * ta)) → tp
  14. Intersect(tc, th, 2) → TD
  15. Intersect(tc, tf) → TE,
  16. Intersect(tp, tg, 2) → TF
  17. Intersect(tp, th) → TG,
  18. Intersect(te, tf, 2) → TH
  19. Intersect(te, tg) → TI,
  20. CircleSector(TA, TD, TE) → tsec1
  21. CircleSector(TB, TH, TI) → tsec2
  22. Vector(TA, TA') → tu
  23. CircleSector(TC, TF, TG) → tsec3
  24. Translate(tsec1, tu) → tsec1'
  25. Vector(TB, TB') → tv
  26. Translate(tsec2, tv) → tsec2'
  27. Vector(TC, TC') → tw
  28. Translate(tsec3, tw) → tsec3'
  29. Segment(QA, QB) → qf
  30. Segment(QB, QC) → qg
  31. Segment(QC, QD) → qh
  32. Segment(QD, QA) → qi
  33. Min({qf, qg, qh, qi}) → qa
  34. Circle(QA, (0.15 * qa)) → qc
  35. Circle(QB, (0.15 * qa)) → qe
  36. Circle(QC, (0.15 * qa)) → qk
  37. Circle(QD, (0.15 * qa)) → qp
  38. Ray(QA, QB) → qj
  39. Ray(QB, QC) → ql
  40. Ray(QC, QD) → qm
  41. Ray(QD, QA) → qn
  42. Intersect(qc, qn, 2) → QE
  43. Intersect(qc, qf) → QF,
  44. Intersect(qe, ql) → QG,
  45. Intersect(qe, qj, 2) → QH
  46. Intersect(qk, ql, 2) → QI
  47. Intersect(qk, qm) → QK,
  48. Intersect(qp, qm, 2) → QL
  49. Intersect(qp, qi) → QM,
  50. CircleSector(QA, QF, QE) → qsec1
  51. CircleSector(QB, QG, QH) → qsec2
  52. CircleSector(QC, QK, QI) → qsec3
  53. CircleSector(QD, QM, QL) → qsec4
  54. Dilate(QA, If[0 < d ≤ 1, 1 - d, 0], J) → QA'
  55. Dilate(QB, If[0 < d ≤ 1, 1 - d, 0], J) → QB'
  56. Dilate(QC, If[0 < d ≤ 1, 1 - d, 0], J) → QC'
  57. Dilate(QD, If[0 < d ≤ 1, 1 - d, 0], J) → QD'
  58. Vector(QA, QA') → qu
  59. Vector(QB, QB') → qv
  60. Vector(QC, QC') → qw
  61. Vector(QD, QD') → qb
  62. Translate(qsec4, qb) → qsec4'
  63. Translate(qsec1, qu) → qsec1'
  64. Translate(qsec2, qv) → qsec2'
  65. Translate(qsec3, qw) → qsec3'
  66. Segment(PA, PB) → pf
  67. Segment(PB, PC) → pg
  68. Segment(PC, PD) → ph
  69. Segment(PD, PE) → p_i
  70. Segment(PE, PA) → pj
  71. Min({pf, pg, ph, p_i, pj}) → pa
  72. Circle(PA, (0.2 * pa)) → pc
  73. Circle(PB, (0.2 * pa)) → pe
  74. Circle(PC, (0.2 * pa)) → pk
  75. Circle(PD, (0.2 * pa)) → pp
  76. Circle(PE, (0.2 * pa)) → pq
  77. Intersect(pc, pf) → PF,
  78. Intersect(pe, pg) → PG,
  79. Intersect(pk, ph) → PH,
  80. Intersect(pp, p_i) → PI,
  81. Intersect(pq, pj) → PK,
  82. Ray(PE, PA) → pl
  83. Ray(PA, PB) → pm
  84. Ray(PB, PC) → pn
  85. Ray(PC, PD) → pr
  86. Ray(PD, PE) → ps
  87. Intersect(pc, pl, 2) → PL
  88. Intersect(pe, pm, 2) → PM
  89. Intersect(pk, pn, 2) → PN
  90. Intersect(pp, pr, 2) → PO
  91. Intersect(pq, ps, 2) → PP
  92. CircleSector(PA, PF, PL) → psec5
  93. CircleSector(PB, PG, PM) → psec1
  94. CircleSector(PC, PH, PN) → psec2
  95. CircleSector(PD, PI, PO) → psec3
  96. CircleSector(PE, PK, PP) → psec4
  97. Dilate(PA, If[0 < d ≤ 1, 1 - d, 0], J) → PA'
  98. Dilate(PB, If[0 < d ≤ 1, 1 - d, 0], J) → PB'
  99. Dilate(PC, If[0 < d ≤ 1, 1 - d, 0], J) → PC'
  100. Dilate(PD, If[0 < d ≤ 1, 1 - d, 0], J) → PD'
  101. Dilate(PE, If[0 < d ≤ 1, 1 - d, 0], J) → PE'
  102. Vector(PA, PA') → pu
  103. Translate(psec5, pu) → psec5'
  104. Vector(PB, PB') → pv
  105. Translate(psec1, pv) → psec1'
  106. Vector(PC, PC') → pw
  107. Translate(psec2, pw) → psec2'
  108. Vector(PD, PD') → pb
  109. Translate(psec3, pb) → psec3'
  110. Vector(PE, PE') → pu_1
  111. Translate(psec4, pu_1) → psec4'
  112. Segment(HA, HB) → hf
  113. Segment(HB, HC) → hg
  114. Segment(HC, HD) → hh
  115. Segment(HD, HE) → hi
  116. Segment(HE, HF) → hj
  117. Segment(HF, HA) → hk
  118. Min({hf, hg, hh, hi, hj, hk}) → a
  119. Circle(HA, (0.2 * a)) → hc
  120. Circle(HB, (0.2 * a)) → he
  121. Circle(HC, (0.2 * a)) → hp
  122. Circle(HD, (0.2 * a)) → hq
  123. Circle(HE, (0.2 * a)) → hr
  124. Circle(HF, (0.2 * a)) → hs
  125. Intersect(hc, hf) → HG,
  126. Intersect(he, hg) → HH,
  127. Intersect(hp, hh) → HI,
  128. Intersect(hq, hi) → HK,
  129. Intersect(hr, hj) → HL,
  130. Intersect(hs, hk) → HM,
  131. Ray(HA, HB) → hl
  132. Ray(HB, HC) → hm
  133. Ray(HC, HD) → hn
  134. Ray(HD, HE) → ht
  135. Ray(HE, HF) → hb
  136. Ray(HM, HA) → hf_1
  137. Intersect(hc, hf_1, 2) → HN
  138. Intersect(he, hl, 2) → HO
  139. Intersect(hp, hm, 2) → HP
  140. Intersect(hq, hn, 2) → HQ
  141. Intersect(hr, ht, 2) → HR
  142. Intersect(hs, hb, 2) → HS
  143. CircleSector(HA, HG, HN) → hsec1
  144. CircleSector(HB, HH, HO) → hsec2
  145. CircleSector(HC, HI, HP) → hsec3
  146. CircleSector(HD, HK, HQ) → hsec4
  147. CircleSector(HE, HL, HR) → hsec5
  148. CircleSector(HF, HM, HS) → hsec6
  149. Dilate(HA, If[0 < d ≤ 1, 1 - d, 0], J) → HA'
  150. Dilate(HB, If[0 < d ≤ 1, 1 - d, 0], J) → HB'
  151. Dilate(HC, If[0 < d ≤ 1, 1 - d, 0], J) → HC'
  152. Dilate(HD, If[0 < d ≤ 1, 1 - d, 0], J) → HD'
  153. Dilate(HE, If[0 < d ≤ 1, 1 - d, 0], J) → HE'
  154. Dilate(HF, If[0 < d ≤ 1, 1 - d, 0], J) → HF'
  155. Vector(HA, HA') → u
  156. Translate(hsec1, u) → hsec1'
  157. Vector(HB, HB') → v
  158. Translate(hsec2, v) → hsec2'
  159. Vector(HC, HC') → w
  160. Translate(hsec3, w) → hsec3'
  161. Vector(HD, HD') → b
  162. Translate(hsec4, b) → hsec4'
  163. Vector(HE, HE') → c
  164. Translate(hsec5, c) → hsec5'
  165. Vector(HF, HF') → e
  166. Translate(hsec6, e) → hsec6'