If point C is the midpoint of both BD and AE, what additional information would you need to be able to state

Question

that AABC = AEDC by the SAS
Congruence Theorem?
(1 point)
O LACB ~ LECD
O BC ~ DC
O AB~ ED
O LA~ LE

Answer 1

To use the SAS (Side-Angle-Side) Congruence Theorem to prove that triangles AABC and AEDC are congruent, you need:

1. Two sides of one triangle to be equal to two sides of the other triangle.
2. The included angle between those two sides to be equal for both triangles.

Since point C is the midpoint of both lines BD and AE, you already have that AC = EC and BC = DC.

However, to apply the SAS theorem, you need one of the following:

• The angles \(\angle ACB\) and \(\angle ECD\) to be equal (which would mean you know that the angles are equal, option given as O LACB ~ LECD).
• You need to show one side from triangle AABC is equal to one side from triangle AEDC (option O AB ~ ED).

Out of your options, the most direct one to satisfy the conditions of SAS is:

• O AB ~ ED - this establishes one pair of equal sides directly.

Therefore, the answer you need is:

O AB ~ ED.