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(Euclid I.32)
(Euclid I.32)
If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles
If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles
Consider triangle ABC
Draw CE parallel to BA
^BAC = ^ACE (Alt. angles in parallel lines)
^ABC = ^ECD (Corr. angles in parallel lines)
So ^ACD = ^ACE + ^ECD
So the whole exterior angle is equal to the sum of the opp. interior angles
So Sum of all interior angles
= ^ABC + ^BCA + ^CAB = ^ACD + ^BCA (Proven above)
= 2 rt. angles (BCD straight line)
Created 24th July 2008
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