Triangle ABC and triangle DEF are two triangles such that AB, BC are respectively equal and parallel to DE, EF. Show that AC is equal and parallel to DF

Asked by Paresh | 11th Dec, 2015, 02:29: 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.
C o n s i d e r space t h e space t r i a n g l e s space A B C space a n d space D E F. G i v e n space t h a t space A B space i s space p a r a l l e l space t o space D E space a n d space B C space i s space p a r a l l e l space t o space E F. J o i n space B E space a n d space A D S i n c e space A B equals C D comma space a n d space A B parallel to D E comma space A B D E space i s space a space p a r a l l e log r a m. rightwards double arrow A D equals B E... left parenthesis 1 right parenthesis  J o i n space C F. S i n c e space B C equals E F comma space a n d space B C parallel to E F comma space B C F E space i s space a space p a r a l l e l o g r a m. rightwards double arrow C F equals B E... left parenthesis 2 right parenthesis C o m p a r i n g space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma A D equals B E equals C F rightwards double arrow A D F C space i s space a space p a r a l l e log r a m. rightwards double arrow O p p o s i t e space s i d e s space o f space t h e space p a r a l l e log r a m space a r e space e q u a l rightwards double arrow A C equals D F

Answered by Vimala Ramamurthy | 11th Dec, 2015, 07:19: PM