Question

abcd is a parallelogram the bisectorof d and c meet at pt p of side ab prove p is a mid pt of,side ab​

Answer 1

Step-by-step explanation:

ABCD is a parallelogram. Mid-point of BC is E

⇒ Join A to E, ∠EAD=∠EAB ----- ( 1 )

⇒ AD is parallel to BC and AE is a transversal

∴ ∠EAD=∠BEA ----- ( 2 ) [Alternate angle]

⇒ ∠EAB=∠BEA [From ( 1 ) and ( 2 )]

∴ AB=BE ---- ( 3 )

⇒ But BE=

2

BC

=

2

AD

---- ( 4 )

⇒ Put value of BE in equation ( 3 )

∴ AB=AD

2

1

HENCE PROVED ..