Question

Can someone please help me with this proof?!

Given: AC and BD bis, each other.

Prove: ABCD is a parallelogram

Answer 1

because AC and BD bis => AX = XC; BX = XD

ΔAXD ≅ ΔCXB (SAS) because: AX = CX

DX = BX

m∠AXD = m∠BXC ( 2 opposing angles)

because ΔAXD ≅ ΔCXB (SAS)

=> AD = BC and m∠DAX = m∠BCX

because m∠DAX = m∠BCX => AD//BC

ABCD has AD = BC and AD//BC => ABCD is a parallelogram

Explanation: