Question
Fri March 13, 2015 By: Archita Srivastava

ABCD is a square. M is a point on AB such that AM=MB. P&Q are points on sides AD & extended CB such that CM is perpendicular to PQ. Show that ar(CPM)=(CQM)

Expert Reply
Vimala Ramamurthy
Sat March 14, 2015
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 triangle A P M space a n d triangle B Q M angle A M P equals angle B M Q space space space space space left square bracket v e r t i c a l l y space o p p o s i t e space a n g l e s space a r e space e q u a l right square bracket A M equals M B space space space space space space space space space space space space space space space space space left square bracket g i v e n right square bracket angle M A P equals angle M B Q equals 90 degree space space space space left square bracket A B C D space i s space a space s q u a r e comma space h e n c e space c o r r n e r space a n g l e s space a r e space r i g h t space a n g l e s right square bracket 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 triangle A P M approximately equal to triangle B Q M T h e space c o r r e s p o n d i n g space p a r t s space o f space t h e space c c o n g r u e n t space t r i a n g l e s space a r e space c o n g r u e n t. T h u s comma space b y space c p c t comma space P M equals Q M  J o i n space C P N o w space c o n s i d e r space t h e space t r i a n g l e s space triangle C P M space a n d space triangle C Q M C M equals C M space space space space left square bracket c o m m o n angle C M P equals angle C M Q equals 90 degree space space space space left square bracket g i v e n right square bracket P M equals Q M space space space space space left square bracket f r o m space e q u a t i o n space left parenthesis 1 right parenthesis right square bracket T h u s comma space w e space h a v e comma triangle C P M space approximately equal to space triangle C Q M C o n c g r u e n t space t r a i n g l e s space h a v e space e q u a l space a r e a s comma space h e n c e space A r e a open parentheses triangle C P M close parentheses space equals A r e a space open parentheses triangle C Q M close parentheses
Home Work Help