Answer: [tex]A.\ \triangle{ABX}\cong\triangle{DEX}[/tex]
Step-by-step explanation:
In the given picture , we have given that X is the midpoint of [tex]\overline{AD}[/tex] and [tex]\overline{BE}[/tex] .
i.e. AX = XD and BX=XE (1)
Then in [tex]\triangle{ABX}[/tex] and [tex]\triangle{DEX}[/tex], we have
[tex]\angle{AXB}\cong\angle{EXD}[/tex] [∵ Vertical angles are congruent ]
AX = XD and BX=XE [from (1)]
So by SAS postulate of congruence , we have
[tex]\triangle{ABX}\cong\triangle{DEX}[/tex]
