Question

Plz explain and prove the triangles congruence.

Answer 1

Answer:

4) $\overline{BD}\ and\ \overline{AC} \ \textrm{bisect each other.}$

Step-by-step explanation:

Given:

$\overline{BD}\ and\ \overline{AC} \ \textrm{bisect each other}$

AE =EC  and

BE = DE

To Prove:

Δ ABE ≅ ΔCDE

Proof:

$In\ \triangle ABE\ and\ \triangle CDE\\\overline{AE} \cong \overline{CE}\ \textrm{Given BD and AC bisect each other}\\ \angle AEB \cong \angle CED\ \textrm{vertically opposite angles}\\ \overline{BE} \cong \overline{DE}\ \textrm{Given BD and AC bisect each other}\\ \therefore \triangle ABE \cong \triangle CDE\ \textrm{By Side-Angle-Side test...PROVED}$.

Hence,

4) $\overline{BD}\ and\ \overline{AC} \ \textrm{bisect each other.}$

sufficient to prove Δ ABE ≅ ΔCDE .