Question

If BD bisects AC and AC bisects BD, is ABE ≅ CDE? Explain.

Answer 1

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:

$AE = CE$ --- Side

and

$BE = DE$ --- Side

When both lines bisect one another, they form a pair of vertical angles $\angle AEB$ and $\angle CED$

When we apply the theorem of vertical angles to this, we have that:

$\angle AEB$ $=$ $\angle CED$ --- 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.