Question

X
12. In Fig. 11.38, ABCD is a parallelogram whose
diagonals intersect each other at P. XY, a line
segment, passes through P. Give reasons for each
of the following:
(a) PB = PD
(b) ZPBY = ZPDX
(c) ZBPY = ZDPX
(d) ABPY = ADPX
(e) PY = PX


please help me!!​

Answer 1

Answer:

by CPCT

Step-by-step explanation:

We know that ABCD is a parallelogram whose diagonals intersect each other at O

Consider △AOE and △COF

We know that ∠CAE and ∠DCA are alternate interior angles

⟹∠CAE=∠DCA

From the figure we know that the diagonals are equal and bisect each other

⟹AO=CO

We know that ∠AOE and ∠COF are vertically opposite angles

⟹∠AOE=∠COF

By ASA congruence criterion

△AOE≅COF

⟹OE=OF (By C.P.C.T)