Question

Fill in the missing information:

Given that C is a midpoint of both segments BD and AE. Therefore BC = DC and AC = EC based on the ________.

Using the vertical angle theorem, _________.

In conclusion, △ABC ≅ △EDC by the _________.

A. Corresponding sides, vertical angles, SAS congruence postulate
B. Corresponding angles, vertical angles, ASA congruence postulate
C. Corresponding sides, adjacent angles, ASA congruence postulate
D. Corresponding angles, vertical angles, SAS congruence postulate

Answer 1

The triangles ABC and EDC are congruent using corresponding sides, vertical angles, and SAS congruence postulate.

Step-by-step explanation:

Based on the given information, we can conclude that the triangles ABC and EDC are congruent. This can be proven using the corresponding sides, vertical angles, and SAS congruence postulate.

First, since C is the midpoint of BD, we know that BC = DC. Similarly, since C is the midpoint of AE, AC = EC.

Next, using the vertical angle theorem, we can determine that the angles ∠ABC and ∠EDC are congruent.

Finally, since BC = DC, AC = EC, and ∠ABC = ∠EDC, we can apply the SAS congruence postulate to prove that the triangles ABC and EDC are congruent.