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多边形外角 by Heather Pierce

多边形外角 by Heather Pierce
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2018-12-04 23:40
多边形角几何作图
①本范例演示多边形外角的性质与计算；②涉及核心概念包括外角和定理、多边形内角与外角关系；③构造要点：使用 GeoGebra 命令如 Dilate（缩放）、Ray（射线）、Segment（线段）、Min（最小值）、Circle（圆）、Intersect（交点）、CircleSector（扇形）、Vector（向量）、Translate（平移）；对象包括 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（三角形）、quadrilateral（四边形）、pentagon（五边形）、hexagon（六边形）、button1（按钮）、QA、QB；④适合初中及以上学生学习多边形几何性质，或用于数学教学演示。

GeoGebra 命令及参数

  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'