數學證明定理

角和直線:
adj. ∠s on st. line直線上的鄰角
∠s at a pt.同頂角
vert. opp. ∠s對頂角
corr. ∠s, AB//CD同位角
int. ∠s supp.同旁內角

三角形和多邊形的角:
∠ sum of Δ三角形內角和
ext. ∠ of Δ三角形外角和
∠ sum of polygon多邊形內角和
sum of ext. ∠s of polygon多邊形外角和

特別的三角形:
base ∠s, isos.Δ
sides opp. equal ∠s
property of isos. Δ
property of equil. Δ

全等及相似三角形:
corr. ∠s, ~= Δs
corr. sides, ~= Δs
corr. ∠s, ~ Δs
corr. sides, ~ Δs
3 side prop.
ratio of 2 sides, inc.∠

mid-pt. theorem
intercept theorem
base ∠s, isos.Δ 等腰三角形對角相等
sides opp. equal ∠s 等邊對角相等
property of isos. Δ 等腰三角形特性

corr. ∠s, ~= Δs 全等Δ對應角
corr. sides, ~= Δs 全等Δ對應邊
corr. ∠s, ~ Δs 相似Δ對應角
corr. sides, ~ Δs 相似Δ對應邊
3 side prop. 三邊成比例
ratio of 2 sides, inc.∠ 兩邊成比例及對角相等

mid-pt. theorem 中點定理
intercept theorem 截線定理

1. Angle sum of triangle = ∠sum of Δ Δ內角和
2. Exterior angle of triangle = ext. ∠ of Δ .Δ外角
3. Pythagoras' theorem = Pyth. theorem 畢氏定理
4. Converse of Pythagoras' theorem = Converse of Pyth. theorem 畢氏定理的逆定理
5. Angle sum of polygon = ∠sum of polygon 多邊形內角和
6. Sum of exterior angles of polygon = sum of ext. ∠s of polygon 多邊形外角和
7. Angles at a point = ∠s at a pt. 同頂角
8. Vertically opposite angles = vert. opp. ∠s 對頂角
9. Adjacent angles on a straight line = adj. ∠s on st. line 直線上的鄰角
10. Corresponding angles 同位角
11. Alternate angles 內錯角
12. Interior angles on the same side 同旁內角
13. Corresponding angles = corr. ∠s, AB//CD 同位角相等
14. Alternate angles = alt. ∠s, AB//CD 內錯角相等
15. Interior angles on the same side = int. ∠s, AB//CD 同旁內角互補
16. Base angles of an isosceles triangle = base ∠s, isos. Δ 等腰Δ底角
17. Equiangular 等角對邊相等
18. Nature of isosceles triangle 等腰Δ性質
19. Nature of equilateral triangle 等邊Δ性質
20. Correspomding sides of congruent triangle 全等Δ的對應邊
21. Corresponding angles of congruent triangle 全等Δ的對應角
22. Corresponding sides of simular triangle 相似Δ的對應邊
23. Corresponding angles of simular triangle 相似Δ的對應角
24. Three sides proportional = 3 sides proportional 三邊成比例
25. Ratio of two sides included angles = ratio of 2 sides, inc. ∠兩邊成比例且夾角相等
26. Angle bisector 角平分線
27. Perpendicular bisector 垂直平分線
28. Median 中線
29. Altitude 頂垂線
30. Common sides 公共邊
31. Common angles 公共角

Congruent triangles:
(S.S.S.) (S.A.S.) (A.A.S) (A.S.A.) (R.H.S)
(corr. sides, △s) (corr.∠s, △s) (common side)

Similar triangles:
(A.A.A.) (ratio of 2 sides, inc.∠s) (3 sides prop.)
(corr. sides, ~△s) (corr.∠s, ~△s) (common ∠)

Isosceles triangles:
(base ∠s, isos. △s) (sides opp. equal ∠s)

Right-angled triangles:
(Pyth. theorem) (converse of Pyth. theorem)

Triangles:
(∠ sum of △) (ext.∠ of △) (prop. of equil.△)

Polygons:
(∠ sum of polygon) (sum of ext.∠ of polygon)

Others:
(adj.∠s on st. line) (vert. opp.∠s) (∠s at a pt.) (AB⊥CD) (given) (proved) (By construction) (intercept theorem) (mid-pt. theorem)

Parallel lines:
(corr.∠s, AB//CD) (alt.∠s, AB//CD) (int.∠s, AB//CD)
(corr.∠s equal) (alt.∠s equal) (int.∠s supp.)

Parallelograms / quadrilaterals:
(opp.∠s of //gram) (opp. sides of //gram) (diags. of //gram)
(opp. sides equal and // ) (opp. sides equal) (opp.∠s equal) (diag. bisect each other)
(property of rectangle) (property of square) (property of rhombus)

Circles:
(radii) (line from centre⊥chord bisects chord) (line joining centre to mid-pt. of chord⊥chord) (equal chords, equidistant from centre) (chord equidistant from centre are equal) (∠at centre twice ∠ at ☉ce) (∠in semi-circle) (∠s in the same segment) (equal ∠s, equal arcs) (equal ∠s, equal chords) (equal arcs, equal ∠s) (equal arcs, equal chords) (equal chords, equal arcs) (equal chords, equal ∠s) (arcs prop. to ∠s at centre) (arcs prop. to ∠s at ☉ce)

Cyclic quadrilaterals:
Uses: (opp. ∠s, cyclic quad.) (ext. ∠s, cyclic quad.)
Tests: (converse of ∠s in the same segment) (opp. ∠s supp.) (ext.∠= int. opp.∠)

Tangents:
(tangent⊥radius) (converse of tangent⊥radius)
(tangent properties)
(∠in alt. segment) (converse of ∠in alt. segment)