Question

4. In the given figure, ABCD is a parallelogram. P is
the mid-point of AB. Prove that ACBM is a
parallelogram.​

Answer 1

ACBM is  a parallelogram if P is the mid point of AB in ABCD parallelogram

Step-by-step explanation:

in ΔBPC & ΔAPM

BP = AP  ( p is mid point)

∠BPC = ∠APM  ( opposite angles)

∠CBP = ∠MAP   ( as CB ║AM)

=> ΔBPC ≅ ΔAPM

=> CP = PM

   CB = AM  

  CB ║AM

so we just need to show that

AC = BM to prove ACBM is  a parallelogram

ΔAPC & ΔBPM

AP = BP

CP = PM

∠APC = ∠BPM  ( opposite angles)

ΔAPC ≅ ΔBPM

=> AC = BM

Hence Proved that ACBM is  a parallelogram

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