Question

ABC, DBC are two triangles in which AC and BD meet at X.
If AX = DX and BX = CX, then which of the following statements are correct?

• A. $\Delta AXB\cong \Delta DXC$ by ASA postulate
• B. $\Delta AXB\cong \Delta DXC$ by SAS postulate
• C. $\angle BAX=\angle CDX$
• D. $AB=CD$

Answer 1

Answer: (B), (C), (D)

The correct options are
B

$\Delta AXB\cong \Delta DXC$ by SAS postulate

C

$\angle BAX=\angle CDX$

D

$AB=CD$

In $\Delta BAX$ and $\Delta CDX$,

AX = DX ………(given)

BX = CX ………(given)

$\angle AXB=\angle DXC$ ……….(vertically opposite angles are equal)

$\Delta BAX\cong \Delta CDX$ …… (SAS postulate)

$\angle BAX=\angle CDX$ ……..(cpct)

AB = CD ……..(cpct)