【醫生爸爸數學課】三角形

adj. ∠s on st. line

adj. ∠s supp.

 

adj. ∠s at a pt

vert. opp. ∠s

 

Parallel lines

corr. ∠s, AB//CD

alt. ∠s, AB//CD

int. ∠s, AB//CD

 

Reasons to prove parallel lines

1. corr. ∠s eq.
2. alt. ∠s eq.
3. int. ∠s supp.

 

Triangles

∠ sum of  ∆

 

ext. ∠  of  ∆

 

base ∠s, isos. ∆

prop. of isos. △
prop. of equil. △  

 

Congruent triangles

corr.  ∠s, = ≅∆s

corr. sides,  ≅∆s

Reasons to prove Congruent Triangles

1. SSS (three pairs of sides of two triangles are correspondingly equal)
2. SAS (two pairs of sides and a pair of included angles of two triangles are correspondingly equal)
3. ASA (two pairs of angles and one pair of sides are correspondingly equal)
4. AAS (two pairs of angles and one pair of sides are correspondingly equal)
5. RHS (one pair of sides and the hypotenuses of two right-angled triangles are correspondingly equal)  

Similar triangles

corr.  ∠s, ~∆s

corr. sides,  ~∆s

equiangular

3 sides proportional

Reasons to prove Similar Triangles 

1. AAA (all angles of two triangles are correspondingly equal)
2. 3 sides prop. (the sides of two triangles are correspondingly proportional)
3. ratio of 2 sides, inc. ∠ (two sides of two triangles are correspondingly proportional, and their included angles are equal)
   

  

Polygon

∠ sum of polygon
sum of ext. ∠s of polygon  

 

 

Dr. Pierre Chan