i want the basic concepts which is used to prove trignometry prove that sums( not trignometric formulas). Like angle sum property of a triangle.
 

Asked by Rama Subramanian | 5th Jun, 2016, 01:53: PM

Expert Answer:

C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
L e t space A B C space b e space a space t r i a n g l e.
L e t space P Q space b e space a space l i n e space t h a t space p a s s e s space t h r o u g h space A
T h u s space angle P A Q space i s space a space s t r a i g h t space a n g l e
rightwards double arrow angle P A Q equals 180 degree
rightwards double arrow angle P A B plus angle B A C plus angle C A Q equals 180 degree space space space space... left parenthesis 1 right parenthesis
S i n c e space P A Q space i s space p a r a l l e l space t o space B C comma space w e space h a v e comma space A B space a n d space A C space a s space t h e space t r a n s v e r s a l s.
rightwards double arrow angle P A B equals angle A B C space space space... left parenthesis 2 right parenthesis
A n d space s i m i l a r l y comma
angle Q A C equals angle A C B space space space space... left parenthesis 3 right parenthesis
S u b s t i t u t i n g space t h e space v a l u e s space o f space angle P A B space a n d space angle Q A C space f r o m space e q u a t i o n s space left parenthesis 2 right parenthesis space a n d space left parenthesis 3 right parenthesis space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma
angle A B C plus angle B A C plus angle A C B equals 180 degree
T h a t space i s space i n space a space t r i a n g l e comma space w e space h a v e comma
angle A plus angle B plus angle C equals 180 degree

Answered by Vimala | 6th Jun, 2016, 11:12: AM