Answer:
C. Yes; the triangles are congruent by SAS.
Step-by-step explanation:
From the question, we understand that:
AC and BD bisects one another
The bisection is better illustrated with a diagram. (See attachment).
From this point, I'll use the attachment as a point of reference.
From the attachment:
[tex]AE = CE[/tex] --- Side
and
[tex]BE = DE[/tex] --- Side
When both lines bisect one another, they form a pair of vertical angles [tex]\angle AEB[/tex] and [tex]\angle CED[/tex]
When we apply the theorem of vertical angles to this, we have that:
[tex]\angle AEB[/tex] [tex]=[/tex] [tex]\angle CED[/tex] --- Angle
At this point, we have established:
Two sides of ABE and CDE are congruent
and
One angle in each of ABE and CDE are also congruent
Hence, the triangles are congruent by SAS.
