In the given figure, E D parallel to A B, AB = 10CM, BC  = 6CM, AC = 8CM, GE = 3CM. List all similar triangles. How many pairs of similar triangles are possilble?

Asked by vatsalchoudhary41 | 24th Sep, 2015, 06:14: AM

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.
T h e r e space a r e space s i x space t r i a n g l e s space triangle A B C comma space triangle E D F comma space triangle A F G comma space triangle C D H comma space triangle E G C space a n d space triangle B F H. S i n c e space A B space i s space p a r a l l e l space t o space E D space a n d space t h e space c o r n e r space a n g l e s space o f space t h e space p a r a l l e log r a m space G C H F G space a r e space 90 degree comma a l l space t h e space t r i a n g l e s space triangle A B C comma space triangle E D F comma space triangle A F G comma space triangle C D H comma space triangle E G C space a n d space triangle B F H space a r e space s i m i l a r space t o space e a c h space o t h e r. W e space n e e d space t o space s e l e c t space p a i r space o f space t r i a n g l e s space f r o m space t h e space c o l l e c t i o n space o f space 6. T h u s comma space t h e r e space a r e space C presuperscript 6 subscript 2 space w a y s space o f space s e l e c t i n g space t h e space p a i r s. H e n c e comma space C presuperscript 6 subscript 2 equals fraction numerator 6 cross times 5 over denominator 1 cross times 2 end fraction equals 15 T h e r e f o r e comma space t h e r e space a r e space 15 space p a i r s space o f space s i m i l a r space t r i a n g l e s. S i m i l a r space t r i a n g l e s space a r e colon triangle A B C tilde triangle E F D triangle A B C tilde triangle E G C triangle A B C tilde triangle C D H triangle A B C tilde triangle B F H triangle A B C tilde triangle A G F  triangle E F D tilde triangle E G C triangle E F D tilde triangle C D H triangle E F D tilde triangle B F H triangle E F D tilde triangle A G F  triangle E G C tilde triangle C D H triangle E G C tilde triangle B F H triangle E G C tilde triangle A G F  triangle C D H tilde triangle B F H triangle C D H tilde triangle A G F  triangle B F H tilde triangle A G F
 

Answered by Vimala Ramamurthy | 24th Sep, 2015, 11:13: AM

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