Question

In a AABC median AD is produced to P such that
AD = DP. Prove that ABPC is a parallelogram​

Answer 1

Answer:

given- AD=DP AND BD=CD

sol- in ΔADB AND ΔPCD

            AD=DP

            BD=DC

            ∠ADB=∠PCD   (VOA)

         ΔADB≅ΔPCD  (SAS)

         AB=PC  (CPCT)         (1)

SIMILARLY, ΔADC≅ΔPDB

AND AC=BP (CPCT) (2)

SINCE DIAGONALS BISECT EACH OTHER (GIVEN)

AND OPP SIDES ARE EQUAL(FROM 1 AND 2)

ABPC IS A PARALLELOGRAM

Step-by-step explanation: