CBSE Class 7 Answered

Can you explain me the congruence criterion??briefly.

Asked by Shreelakshmi | 15 Nov, 2015, 03:55: PM

Expert Answer

1. space S S S minus S i d e minus S i d e minus S i d e space c r i t e r i o n space o f space c o n g r u e n c e space space space T w o space T r i a n g l e s space a r e space c o n g r u e n t space i f space a l l space t h r e e space s i d e s space i n space o n e space t r i a n g l e space a r e space c o n g r u e n t space t o space t h e space c o r r e s p o n d i n g space s i d e s space i n space t h e space o t h e r. O b s e r v e space t h e space f o l l o w i n g space f i g u r e. space space

I n space t h e space a b o v e space f i g u r e comma space A B equals P Q comma space A C equals P R space a n d space B C equals Q R H e n c e space b y space S i d e minus S i d e minus S i d e space c r i t e r i o n space o f space c o n g r u e n c e comma space t r i a n g l e s space triangle A B C space a n d space triangle P Q R space a r e space c o n g r u e n t.

space 2. space A S A minus A n g l e minus S i d e minus A n g l e space c r i t e r i o n space o f space c o n g r u e n c e space space space T w o space T r i a n g l e s space a r e space c o n g r u e n t space i f space t w o space a n g l e s space a n d space a n space i n c l u d e d space s i d e space i n space o n e space t r i a n g l e space a r e space c o n g r u e n t space t o space t h e space c o r r e s p o n d i n g space a n g l e s space a n d space s i d e space i n space t h e space o t h e r. space O b s e r v e space t h e space f o l l o w i n g space f i g u r e.

I n space t h e space a b o v e space f i g u r e comma space angle A equals angle P space A B equals P Q angle B equals angle Q T h u s comma space b y space A n g l e minus S i d e minus A n g l e space c r i t e r i o n space o f space c o n g r u e n c e comma space w e space h a v e comma space triangle A B C asymptotically equal to triangle P Q R

3. space R H S minus R i g h t space A n g l e minus H y p o t e n u s e minus S i d e space c r i t e r i o n space o f space c o n g r u e n c e space space space T w o space r i g h t minus a n g l e d space t r i a n g l e s space a r e space c o n g r u e n t space i f space t h e space h y p o t e n u s e s space a n d space o n e space p a i r space o f space c o r r e s p o n d i n g space s i d e s space a r e space e q u a l. O b s e r v e space t h e space f o l l o w i n g space f i g u r e.

I n space t h e space a b o v e space f i g u r e comma space b o t h space t h e space t r i a n g l e s space triangle A B C space a n d space triangle P Q R space a r e space r i g h t space t r i a n g l e s space a t space B space a n d space Q space r e s p e c t i v e l y. A l s o space A C equals P R space a n d space A B equals P Q H e n c e comma space b y space R i g h t space a n g l e minus H y p o t e n u s e minus S i d e space c r i t e r i o n space o f space c o n g r u e n c e comma space w e space h a v e comma triangle A B C asymptotically equal to triangle P Q R.

4. A A S minus A n g l e minus A n g l e minus S i d e space c r i t e r i o n space o f space c o n g r u e n c e colon T w o space a n g l e s space a n d space a space n o n minus i n c l u d e d space s i d e space o f space o n e space t r i a n g l e space a r e space c o n g r u e n t space t o space t h e space c o r r e s p o n d i n g p a r t s space o f space a n o t h e r space t h r i a n g l e comma space t h e n space t h e space t r i a n g l e s space a r e space c o n g r u e n t. O b s e r v e space t h e space f o l l o w i n g space f i g u r e.

I n space t h e space a b o v e space f i g u r e comma space angle A equals angle P angle B equals angle Q a n d A C equals P R H e n c e comma space b y space A n g l e minus A n g l e minus S i d e space c r i t e r i o n space o f space c o n g r u e n c e comma space w e space h a v e comma triangle A B C asymptotically equal to triangle P Q R

Answered by Vimala Ramamurthy | 16 Nov, 2015, 11:27: AM

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