由 Raceleader 於 星期三 四月 09, 2003 10:27 am
Property of equilateral triangle
If ABC is an equilateral triangle, then AB=BC=CA and ∠ABC=∠BCA=∠CAB=60° (Property of equilateral triangle)
Proof
△ABC is an equilateral triangle (Given)
∴The triangle has three equal sides (By definition)
∴AB=BC=CA
∵AB=BC=CA (Prove)
∴∠ABC=∠ACB (Base angles of isosceles triangle)
∴∠BAC=∠BCA (Base angles of isosceles triangle)
∴∠ABC=∠BCA=∠CAB
∵∠ABC+∠BCA+∠CAB=180° (Angle sum of triangle)
∴3∠ABC=180°
∴∠ABC=∠BCA=∠CAB=60°
If AB=BC=CA or ∠ABC=∠BCA=∠CAB=60°, then △ABC is an equilateral triangle